In this article, we study a least squares estimator (LSE) of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt+dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain...In this article, we study a least squares estimator (LSE) of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt+dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.展开更多
Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric...Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ,we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that itimproves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given todetermine the number of iterations. We also show that when the number of replicates is less than orequal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of thosein [2] to the case of semiparametric regressions.展开更多
We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes dY_(s)=(∑_(j=1)^(k)μ_(j)φ_(j)(s)-βY_(s))ds+dZ_(s)^(q,H),driven by the Hermite process Z_(s)^(q,H)with order q≥1 and a Hurs...We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes dY_(s)=(∑_(j=1)^(k)μ_(j)φ_(j)(s)-βY_(s))ds+dZ_(s)^(q,H),driven by the Hermite process Z_(s)^(q,H)with order q≥1 and a Hurst index H∈(1/2,1),where the periodic functionsφ_(j)(s),,j=1,...,κare bounded,and the real numbersμ_(j),,j=1,...,κtogether withβ>0 are unknown parameters.We establish the consistency of a least squares estimation and obtain the asymptotic behavior for the estimator.We also introduce alternative estimators,which can be looked upon as an application of the least squares estimator.In terms of the fractional Ornstein-Uhlenbeck processes with periodic mean,our work can be regarded as its non-Gaussian extension.展开更多
This paper discusses comparison of two time series decomposition methods: The Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. As noted by Iwueze and Nwogu (2014), there exists a research gap f...This paper discusses comparison of two time series decomposition methods: The Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. As noted by Iwueze and Nwogu (2014), there exists a research gap for the choice of appropriate model for decomposition and detection of presence of seasonal effect in a series model. Estimates of trend parameters and seasonal indices are all that are needed to fill the research gap. However, these estimates are obtainable through the Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. Hence, there is need to compare estimates of the two methods and recommend. The comparison of the two methods is done using the Accuracy Measures (Mean Error (ME)), Mean Square Error (MSE), the Mean Absolute Error (MAE), and the Mean Absolute Percentage Error (MAPE). The results from simulated series show that for the additive model;the summary statistics (ME, MSE and MAE) for the two estimation methods and for all the selected trending curves are equal in all the simulations both in magnitude and direction. For the multiplicative model, results show that when a series is dominated by trend, the estimates of the parameters by both methods become less precise and differ more widely from each other. However, if conditions for successful transformation (using the logarithmic transform in linearizing the multiplicative model to additive model) are met, both of them give similar results.展开更多
BACKGROUND Iterative decomposition of water and fat with echo asymmetry and least squares estimation quantification sequence(IDEAL-IQ)is based on chemical shift-based water and fat separation technique to get proton d...BACKGROUND Iterative decomposition of water and fat with echo asymmetry and least squares estimation quantification sequence(IDEAL-IQ)is based on chemical shift-based water and fat separation technique to get proton density fat fraction.Multiple studies have shown that using IDEAL-IQ to test the stability and repeatability of liver fat is acceptable and has high accuracy.AIM To explore whether Gadoxetate Disodium(Gd-EOB-DTPA)interferes with the measurement of the hepatic fat content quantified with the IDEAL-IQ and to evaluate the robustness of this technique.METHODS IDEAL-IQ was used to quantify the liver fat content at 3.0T in 65 patients injected with Gd-EOB-DTPA contrast.After injection,IDEAL-IQ was estimated four times,and the fat fraction(FF)and R2* were measured at the following time points:Precontrast,between the portal phase(70 s)and the late phase(180 s),the delayed phase(5 min)and the hepatobiliary phase(20 min).One-way repeated-measures analysis was conducted to evaluate the difference in the FFs between the four time points.Bland-Altman plots were adopted to assess the FF changes before and after injection of the contrast agent.P<0.05 was considered statistically significant.RESULTS The assessment of the FF at the four time points in the liver,spleen and spine showed no significant differences,and the measurements of hepatic FF yielded good consistency between T1 and T2[95%confidence interval:-0.6768%,0.6658%],T1 and T3(-0.3900%,0.3178%),and T1 and T4(-0.3750%,0.2825%).R2* of the liver,spleen and spine increased significantly after injection(P<0.0001).CONCLUSION Using the IDEAL-IQ sequence to measure the FF,we can obtain results that will not be affected by Gd-EOB-DTPA.The high reproducibility of the IDEAL-IQ sequence makes it available in the scanning interval to save time during multiphase examinations.展开更多
In this paper, we have studied the nonparameter accelerated failure time (AFT) additive regression model, whose covariates have a nonparametric effect on high-dimensional censored data. We give the asymptotic property...In this paper, we have studied the nonparameter accelerated failure time (AFT) additive regression model, whose covariates have a nonparametric effect on high-dimensional censored data. We give the asymptotic property of the penalty estimator based on GMCP in the nonparameter AFT model.展开更多
Software reliability growth models (SRGMs) incorporating the imperfect debugging and learning phenomenon of developers have recently been developed by many researchers to estimate software reliability measures such ...Software reliability growth models (SRGMs) incorporating the imperfect debugging and learning phenomenon of developers have recently been developed by many researchers to estimate software reliability measures such as the number of remaining faults and software reliability. However, the model parameters of both the fault content rate function and fault detection rate function of the SRGMs are often considered to be independent from each other. In practice, this assumption may not be the case and it is worth to investigate what if it is not. In this paper, we aim for such study and propose a software reliability model connecting the imperfect debugging and learning phenomenon by a common parameter among the two functions, called the imperfect-debugging fault-detection dependent-parameter model. Software testing data collected from real applications are utilized to illustrate the proposed model for both the descriptive and predictive power by determining the non-zero initial debugging process.展开更多
The parametric estimation problem for diffusion processes with small white noise based on continuous time observations is well developed. However,in parametric inference,it is more realistic and interesting to conside...The parametric estimation problem for diffusion processes with small white noise based on continuous time observations is well developed. However,in parametric inference,it is more realistic and interesting to consider asymptotic estimation for diffusion processes based on discrete observations. The least squares method is used to obtain the estimator of the drift parameter for stochastic differential equations( SDEs) driven by general Lévy noises when the process is observed discretely. Its strong consistency and the rate of convergence of the squares estimator are studied under some regularity conditions.展开更多
A time series x(t), t≥1, is said to be an unstable ARMA process if x(t) satisfies an unstableARMA model such asx(t)=a_1x(t-1)+a_2x(t-2)+…+a_8x(t-s)+w(t)where w(t) is a stationary ARMA process; and the characteristic...A time series x(t), t≥1, is said to be an unstable ARMA process if x(t) satisfies an unstableARMA model such asx(t)=a_1x(t-1)+a_2x(t-2)+…+a_8x(t-s)+w(t)where w(t) is a stationary ARMA process; and the characteristic polynomial A(z)=1-a_1z-a_2z^2-…-a_3z^3 has all roots on the unit circle. Asymptotic behavior of sum form 1 to n (x^2(t)) will be studied by showing somerates of divergence of sum form 1 to n (x^2(t)). This kind of properties Will be used for getting the rates of convergenceof least squares estimates of parameters a_1, a_2,…, a_?展开更多
A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, local to unity process, unit root proces...A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, local to unity process, unit root process, mildly integrated, mildly explosive and explosive processes. It is assumed that the cross-sectional dimension and time-series dimension are respectively N and T. The results in this paper illustrate that whichever the process is, with an appropriate regularization, the least squares estimator of the autoregressive coefficient converges in distribution to a normal distribution with rate at least O(N-1/3). Since the variance is the key to characterize the normal distribution, it is important to discuss the variance of the least squares estimator. We will show that when the autoregressive coefficient ρ satisfies |ρ| < 1, the variance declines at the rate O((NT)-1), while the rate changes to O(N^(-1) T^(-2)) when ρ = 1 and O(N^(-1)ρ^(-2 T+4)) when |ρ| > 1. ρ = 1 is the critical point where the convergence rate changes radically. The transition process is studied by assuming ρ depending on T and going to 1. An interesting phenomenon discovered in this paper is that, in the explosive case, the least squares estimator of the autoregressive coefficient has a standard normal limiting distribution in the panel data case while it may not has a limiting distribution in the univariate time series case.展开更多
Recently, Kundu and Gupta (Metrika, 48:83 C 97, 1998) established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the genera...Recently, Kundu and Gupta (Metrika, 48:83 C 97, 1998) established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the general least squares estimators by using random weights which is called the Bayesian bootstrap or the random weighting method by Rubin (Annals of Statistics, 9:130 C 134, 1981) and Zheng (Acta Math. Appl. Sinica (in Chinese), 10(2): 247 C 253, 1987). A simulation study shows that this approximation works very well.展开更多
We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile m...We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile measures,moments,moment generating function,probability weighted moments,Bonferroni and Lorenz curve,stochastic ordering,incomplete moments,residual life function,and entropy measure.Acceptance sampling plans are developed for the PITL distribution,when the life test is truncated at a pre-specified time.The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors.The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk.Numerical results for given consumer’s risk,parameters of the PITL distribution and the truncation time are obtained.The estimation of the model parameters is argued using maximum likelihood,least squares,weighted least squares,maximum product of spacing and Bayesian methods.A simulation study is confirmed to evaluate and compare the behavior of different estimates.Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions.The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.展开更多
VVc deal with the least squares estimator for the drift parameters of an Ornstein-Uhlenbeck process with periodic mean function driven by fractional Levy process.For this estimator,we obtain consistency and the asympt...VVc deal with the least squares estimator for the drift parameters of an Ornstein-Uhlenbeck process with periodic mean function driven by fractional Levy process.For this estimator,we obtain consistency and the asymptotic distribution.Compared with fractional Ornstein-Uhlenbeck and Ornstein-Uhlenbeck driven by Levy process,they can be regarded both as a Levy generalization of fractional Brownian motion and a fractional generalization of Levy process.展开更多
The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional ...The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.展开更多
Linear regression models for interval-valued data have been widely studied.Most literatures are to split an interval into two real numbers,i.e.,the left-and right-endpoints or the center and radius of this interval,an...Linear regression models for interval-valued data have been widely studied.Most literatures are to split an interval into two real numbers,i.e.,the left-and right-endpoints or the center and radius of this interval,and fit two separate real-valued or two dimension linear regression models.This paper is focused on the bias-corrected and heteroscedasticity-adjusted modeling by imposing order constraint to the endpoints of the response interval and weighted linear least squares with estimated covariance matrix,based on a generalized linear model for interval-valued data.A three step estimation method is proposed.Theoretical conclusions and numerical evaluations show that the proposed estimator has higher efficiency than previous estimators.展开更多
In this paper,we consider the partial linear regression model y_(i)=x_(i)β^(*)+g(ti)+ε_(i),i=1,2,...,n,where(x_(i),ti)are known fixed design points,g(·)is an unknown function,andβ^(*)is an unknown parameter to...In this paper,we consider the partial linear regression model y_(i)=x_(i)β^(*)+g(ti)+ε_(i),i=1,2,...,n,where(x_(i),ti)are known fixed design points,g(·)is an unknown function,andβ^(*)is an unknown parameter to be estimated,random errorsε_(i)are(α,β)-mix_(i)ng random variables.The p-th(p>1)mean consistency,strong consistency and complete consistency for least squares estimators ofβ^(*)and g(·)are investigated under some mild conditions.In addition,a numerical simulation is carried out to study the finite sample performance of the theoretical results.Finally,a real data analysis is provided to further verify the effect of the model.展开更多
Background:Different estimation approaches are frequently used to calibrate mathematical models to epidemiological data,particularly for analyzing infectious disease outbreaks.Here,we use two common methods to estimat...Background:Different estimation approaches are frequently used to calibrate mathematical models to epidemiological data,particularly for analyzing infectious disease outbreaks.Here,we use two common methods to estimate parameters that characterize growth patterns using the generalized growth model(GGM)calibrated to real outbreak datasets.Materials and methods:Data from 31 outbreaks are used to fit the GGM to the ascending phase of each outbreak and estimate the parameters using both least squares(LSQ)and maximum likelihood estimation(MLE)methods.We utilize parametric bootstrapping to construct confidence intervals for parameter estimates.We compare the results including RMSE,Anscombe residual,and 95%prediction interval coverage.We also evaluate the correlation between the estimates from both methods.Results:Comparing LSQ and MLE estimates,most outbreaks have similar parameter estimates,RMSE,Anscombe,and 95%prediction interval coverage.Parameter estimates do not differ across methods when the model yields a good fit to the early growth phase.However,for two outbreaks,there are systematic deviations in model fit to the data that explain differences in parameter estimates(e.g.,residuals represent random error rather than systematic deviation).Conclusion:Our findings indicate that utilizing LSQ and MLE methods produce similar results in the context of characterizing epidemic growth patterns with the GGM,provided that the model yields a good fit to the data.展开更多
We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We o...We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We obtain explicit expressions for themoments,moment-generating function,asymptotic distribution,quantile function,mean deviations and distribution of order statistics.The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study.The applicability of the new model is illustrated by means of a real data set.展开更多
In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least ...In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.展开更多
基金supported by the National Natural Science Foundation of China(11271020)the Distinguished Young Scholars Foundation of Anhui Province(1608085J06)supported by the National Natural Science Foundation of China(11171062)
文摘In this article, we study a least squares estimator (LSE) of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt+dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.
基金supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
文摘Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ,we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that itimproves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given todetermine the number of iterations. We also show that when the number of replicates is less than orequal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of thosein [2] to the case of semiparametric regressions.
基金supported by National Natural Science Foundation of China(12071003).
文摘We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes dY_(s)=(∑_(j=1)^(k)μ_(j)φ_(j)(s)-βY_(s))ds+dZ_(s)^(q,H),driven by the Hermite process Z_(s)^(q,H)with order q≥1 and a Hurst index H∈(1/2,1),where the periodic functionsφ_(j)(s),,j=1,...,κare bounded,and the real numbersμ_(j),,j=1,...,κtogether withβ>0 are unknown parameters.We establish the consistency of a least squares estimation and obtain the asymptotic behavior for the estimator.We also introduce alternative estimators,which can be looked upon as an application of the least squares estimator.In terms of the fractional Ornstein-Uhlenbeck processes with periodic mean,our work can be regarded as its non-Gaussian extension.
文摘This paper discusses comparison of two time series decomposition methods: The Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. As noted by Iwueze and Nwogu (2014), there exists a research gap for the choice of appropriate model for decomposition and detection of presence of seasonal effect in a series model. Estimates of trend parameters and seasonal indices are all that are needed to fill the research gap. However, these estimates are obtainable through the Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. Hence, there is need to compare estimates of the two methods and recommend. The comparison of the two methods is done using the Accuracy Measures (Mean Error (ME)), Mean Square Error (MSE), the Mean Absolute Error (MAE), and the Mean Absolute Percentage Error (MAPE). The results from simulated series show that for the additive model;the summary statistics (ME, MSE and MAE) for the two estimation methods and for all the selected trending curves are equal in all the simulations both in magnitude and direction. For the multiplicative model, results show that when a series is dominated by trend, the estimates of the parameters by both methods become less precise and differ more widely from each other. However, if conditions for successful transformation (using the logarithmic transform in linearizing the multiplicative model to additive model) are met, both of them give similar results.
基金Supported by National Natural Science Foundation of China,No.82272053.
文摘BACKGROUND Iterative decomposition of water and fat with echo asymmetry and least squares estimation quantification sequence(IDEAL-IQ)is based on chemical shift-based water and fat separation technique to get proton density fat fraction.Multiple studies have shown that using IDEAL-IQ to test the stability and repeatability of liver fat is acceptable and has high accuracy.AIM To explore whether Gadoxetate Disodium(Gd-EOB-DTPA)interferes with the measurement of the hepatic fat content quantified with the IDEAL-IQ and to evaluate the robustness of this technique.METHODS IDEAL-IQ was used to quantify the liver fat content at 3.0T in 65 patients injected with Gd-EOB-DTPA contrast.After injection,IDEAL-IQ was estimated four times,and the fat fraction(FF)and R2* were measured at the following time points:Precontrast,between the portal phase(70 s)and the late phase(180 s),the delayed phase(5 min)and the hepatobiliary phase(20 min).One-way repeated-measures analysis was conducted to evaluate the difference in the FFs between the four time points.Bland-Altman plots were adopted to assess the FF changes before and after injection of the contrast agent.P<0.05 was considered statistically significant.RESULTS The assessment of the FF at the four time points in the liver,spleen and spine showed no significant differences,and the measurements of hepatic FF yielded good consistency between T1 and T2[95%confidence interval:-0.6768%,0.6658%],T1 and T3(-0.3900%,0.3178%),and T1 and T4(-0.3750%,0.2825%).R2* of the liver,spleen and spine increased significantly after injection(P<0.0001).CONCLUSION Using the IDEAL-IQ sequence to measure the FF,we can obtain results that will not be affected by Gd-EOB-DTPA.The high reproducibility of the IDEAL-IQ sequence makes it available in the scanning interval to save time during multiphase examinations.
文摘In this paper, we have studied the nonparameter accelerated failure time (AFT) additive regression model, whose covariates have a nonparametric effect on high-dimensional censored data. We give the asymptotic property of the penalty estimator based on GMCP in the nonparameter AFT model.
文摘Software reliability growth models (SRGMs) incorporating the imperfect debugging and learning phenomenon of developers have recently been developed by many researchers to estimate software reliability measures such as the number of remaining faults and software reliability. However, the model parameters of both the fault content rate function and fault detection rate function of the SRGMs are often considered to be independent from each other. In practice, this assumption may not be the case and it is worth to investigate what if it is not. In this paper, we aim for such study and propose a software reliability model connecting the imperfect debugging and learning phenomenon by a common parameter among the two functions, called the imperfect-debugging fault-detection dependent-parameter model. Software testing data collected from real applications are utilized to illustrate the proposed model for both the descriptive and predictive power by determining the non-zero initial debugging process.
文摘The parametric estimation problem for diffusion processes with small white noise based on continuous time observations is well developed. However,in parametric inference,it is more realistic and interesting to consider asymptotic estimation for diffusion processes based on discrete observations. The least squares method is used to obtain the estimator of the drift parameter for stochastic differential equations( SDEs) driven by general Lévy noises when the process is observed discretely. Its strong consistency and the rate of convergence of the squares estimator are studied under some regularity conditions.
文摘A time series x(t), t≥1, is said to be an unstable ARMA process if x(t) satisfies an unstableARMA model such asx(t)=a_1x(t-1)+a_2x(t-2)+…+a_8x(t-s)+w(t)where w(t) is a stationary ARMA process; and the characteristic polynomial A(z)=1-a_1z-a_2z^2-…-a_3z^3 has all roots on the unit circle. Asymptotic behavior of sum form 1 to n (x^2(t)) will be studied by showing somerates of divergence of sum form 1 to n (x^2(t)). This kind of properties Will be used for getting the rates of convergenceof least squares estimates of parameters a_1, a_2,…, a_?
基金Supported by the National Natural Science Foundation of China(11871425)Zhejiang Provincial Natural Sci-ence Foundation of China(LY19A010022)the Department of Education of Zhejiang Province(N20140202).
文摘A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, local to unity process, unit root process, mildly integrated, mildly explosive and explosive processes. It is assumed that the cross-sectional dimension and time-series dimension are respectively N and T. The results in this paper illustrate that whichever the process is, with an appropriate regularization, the least squares estimator of the autoregressive coefficient converges in distribution to a normal distribution with rate at least O(N-1/3). Since the variance is the key to characterize the normal distribution, it is important to discuss the variance of the least squares estimator. We will show that when the autoregressive coefficient ρ satisfies |ρ| < 1, the variance declines at the rate O((NT)-1), while the rate changes to O(N^(-1) T^(-2)) when ρ = 1 and O(N^(-1)ρ^(-2 T+4)) when |ρ| > 1. ρ = 1 is the critical point where the convergence rate changes radically. The transition process is studied by assuming ρ depending on T and going to 1. An interesting phenomenon discovered in this paper is that, in the explosive case, the least squares estimator of the autoregressive coefficient has a standard normal limiting distribution in the panel data case while it may not has a limiting distribution in the univariate time series case.
基金Supported by the National Natural Science Foundations of China(No.11271193)Humanities and Social Sciences Planning Foundation of Chinese Ministry of Education(11YJA910004)+1 种基金Natural Science Foundation of the Jiangsu Higher Education Institutions of China(11KJB110005)Key Research Base for Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statistics of Zhejiang Gongshang University)
文摘Recently, Kundu and Gupta (Metrika, 48:83 C 97, 1998) established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the general least squares estimators by using random weights which is called the Bayesian bootstrap or the random weighting method by Rubin (Annals of Statistics, 9:130 C 134, 1981) and Zheng (Acta Math. Appl. Sinica (in Chinese), 10(2): 247 C 253, 1987). A simulation study shows that this approximation works very well.
文摘We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile measures,moments,moment generating function,probability weighted moments,Bonferroni and Lorenz curve,stochastic ordering,incomplete moments,residual life function,and entropy measure.Acceptance sampling plans are developed for the PITL distribution,when the life test is truncated at a pre-specified time.The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors.The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk.Numerical results for given consumer’s risk,parameters of the PITL distribution and the truncation time are obtained.The estimation of the model parameters is argued using maximum likelihood,least squares,weighted least squares,maximum product of spacing and Bayesian methods.A simulation study is confirmed to evaluate and compare the behavior of different estimates.Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions.The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.
基金Guangjun Shen was supported by the Distinguished Young Scholars Foundation of Anhui Province(1608085J06)the Top Talent Project of University Discipline(speciality)(Grant No.gxbjZD03)+2 种基金the National Natural Science Foundation of China(Grant No.11901005)Qian Yu was supported by the ECNU Academic Innovation Promotion Program for Excellent Doctoral Students(YBNLTS2019-010)the Scientific Research Innovation Program for Doctoral Students in Faculty of Economics and Management(2018FEM-BCKYB014).
文摘VVc deal with the least squares estimator for the drift parameters of an Ornstein-Uhlenbeck process with periodic mean function driven by fractional Levy process.For this estimator,we obtain consistency and the asymptotic distribution.Compared with fractional Ornstein-Uhlenbeck and Ornstein-Uhlenbeck driven by Levy process,they can be regarded both as a Levy generalization of fractional Brownian motion and a fractional generalization of Levy process.
基金Key Natural Science Foundation of Anhui Education Commission,China(No.KJ2017A568)Natural Science Foundation of Anhui Province,China(No.1808085MA02)+1 种基金Quality Engineering Project of Anhui Province,China(No.2019jyxm0476)Quality Engineering Project of Bengbu University,China(No.2018JYXML8)。
文摘The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.
基金the National Nature Science Foundation of China under Grant Nos.11571024and 11771032the Humanities and Social Science Foundation of Ministry of Education of China under Grant No.20YJCZH245。
文摘Linear regression models for interval-valued data have been widely studied.Most literatures are to split an interval into two real numbers,i.e.,the left-and right-endpoints or the center and radius of this interval,and fit two separate real-valued or two dimension linear regression models.This paper is focused on the bias-corrected and heteroscedasticity-adjusted modeling by imposing order constraint to the endpoints of the response interval and weighted linear least squares with estimated covariance matrix,based on a generalized linear model for interval-valued data.A three step estimation method is proposed.Theoretical conclusions and numerical evaluations show that the proposed estimator has higher efficiency than previous estimators.
基金Supported by the National Social Science Foundation of China(Grant No.22BTJ059)。
文摘In this paper,we consider the partial linear regression model y_(i)=x_(i)β^(*)+g(ti)+ε_(i),i=1,2,...,n,where(x_(i),ti)are known fixed design points,g(·)is an unknown function,andβ^(*)is an unknown parameter to be estimated,random errorsε_(i)are(α,β)-mix_(i)ng random variables.The p-th(p>1)mean consistency,strong consistency and complete consistency for least squares estimators ofβ^(*)and g(·)are investigated under some mild conditions.In addition,a numerical simulation is carried out to study the finite sample performance of the theoretical results.Finally,a real data analysis is provided to further verify the effect of the model.
基金NSF grant 1414374 as part of the joint NSF-NIH-USDA Ecology and Evolution of Infectious Diseases programUK Biotechnology and Biological Sciences Research Council grant BB/M008894/1.
文摘Background:Different estimation approaches are frequently used to calibrate mathematical models to epidemiological data,particularly for analyzing infectious disease outbreaks.Here,we use two common methods to estimate parameters that characterize growth patterns using the generalized growth model(GGM)calibrated to real outbreak datasets.Materials and methods:Data from 31 outbreaks are used to fit the GGM to the ascending phase of each outbreak and estimate the parameters using both least squares(LSQ)and maximum likelihood estimation(MLE)methods.We utilize parametric bootstrapping to construct confidence intervals for parameter estimates.We compare the results including RMSE,Anscombe residual,and 95%prediction interval coverage.We also evaluate the correlation between the estimates from both methods.Results:Comparing LSQ and MLE estimates,most outbreaks have similar parameter estimates,RMSE,Anscombe,and 95%prediction interval coverage.Parameter estimates do not differ across methods when the model yields a good fit to the early growth phase.However,for two outbreaks,there are systematic deviations in model fit to the data that explain differences in parameter estimates(e.g.,residuals represent random error rather than systematic deviation).Conclusion:Our findings indicate that utilizing LSQ and MLE methods produce similar results in the context of characterizing epidemic growth patterns with the GGM,provided that the model yields a good fit to the data.
文摘We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We obtain explicit expressions for themoments,moment-generating function,asymptotic distribution,quantile function,mean deviations and distribution of order statistics.The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study.The applicability of the new model is illustrated by means of a real data set.
基金Supported by the Educational Commission of Hubei Province of China(Grant No.D20112503)National Natural Science Foundation of China(Grant Nos.11071022,11231010 and 11028103)the foundation of Beijing Center of Mathematics and Information Sciences
文摘In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.