This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations...This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.展开更多
In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribu...In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works;(ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution;(iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Holder continuous) and pathdistribution dependent.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
The least trimmed squares estimator (LTS) is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. We show that the LT...The least trimmed squares estimator (LTS) is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. We show that the LTS estimate can be obtained by a simple algorithm with the complexity 0( N In N) for large N, where N is the number of measurements. We also show that though the LTS is robust in terms of the outliers, it is sensitive to the inliers. The concept of the inliers is introduced. Moreover, the Generalized Least Trimmed Squares estimator (GLTS) together with its solution are presented that reduces the effect of both the outliers and the inliers. Keywords Least squares - Least trimmed squares - Outliers - System identification - Parameter estimation - Robust parameter estimation This work was supported in part by NSF ECS — 9710297 and ECS — 0098181.展开更多
It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this...It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.展开更多
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
Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matri...Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.展开更多
Phasor Measurement Units(PMUs)provide Global Positioning System(GPS)time-stamped synchronized measurements of voltage and current with the phase angle of the system at certain points along with the grid system.Those s...Phasor Measurement Units(PMUs)provide Global Positioning System(GPS)time-stamped synchronized measurements of voltage and current with the phase angle of the system at certain points along with the grid system.Those synchronized data measurements are extracted in the form of amplitude and phase from various locations of the power grid to monitor and control the power system condition.A PMU device is a crucial part of the power equipment in terms of the cost and operative point of view.However,such ongoing development and improvement to PMUs’principal work are essential to the network operators to enhance the grid quality and the operating expenses.This paper introduces a proposed method that led to lowcost and less complex techniques to optimize the performance of PMU using Second-Order Kalman Filter.It is based on the Asyncrhophasor technique resulting in a phase error minimization when receiving the signal from an access point or from the main access point.The MATLAB model has been created to implement the proposed method in the presence of Gaussian and non-Gaussian.The results have shown the proposed method which is Second-Order Kalman Filter outperforms the existing model.The results were tested usingMean Square Error(MSE).The proposed Second-Order Kalman Filter method has been replaced with a synchronization unit into thePMUstructure to clarify the significance of the proposed new PMU.展开更多
In the osmotic dehydration process of food,on-line estimation of concentrations of two components in ternary solution with NaCl and sucrose was performed based on multi-functional sensing technique.Moving Least Square...In the osmotic dehydration process of food,on-line estimation of concentrations of two components in ternary solution with NaCl and sucrose was performed based on multi-functional sensing technique.Moving Least Squares were adopted in approximation procedure to estimate the viscosity of such interested ternary solution with the given data set.As a result,in one mode of using total experimental data as calibration data and validation data,the relative deviations of estimated viscosities are less than ±1.24%.In the other mode,by taking total experimental data except the ones for estimation as calibration data,the relative deviations are less than ±3.47%.In the same way,the density of ternary solution can be also estimated with deviations less than ± 0.11% and ± 0.30% respectively in these two models.The satisfactory and accurate results show the extraordinary efficiency of Moving Least Squares behaved in signal approximation for multi-functional sensors.展开更多
Mobile robot systems performing simultaneous localization and mapping(SLAM) are generally plagued by non-Gaussian noise.To improve both accuracy and robustness under non-Gaussian measurement noise,a robust SLAM algori...Mobile robot systems performing simultaneous localization and mapping(SLAM) are generally plagued by non-Gaussian noise.To improve both accuracy and robustness under non-Gaussian measurement noise,a robust SLAM algorithm is proposed.It is based on the square-root cubature Kalman filter equipped with a Huber' s generalized maximum likelihood estimator(GM-estimator).In particular,the square-root cubature rule is applied to propagate the robot state vector and covariance matrix in the time update,the measurement update and the new landmark initialization stages of the SLAM.Moreover,gain weight matrices with respect to the measurement residuals are calculated by utilizing Huber' s technique in the measurement update step.The measurement outliers are suppressed by lower Kalman gains as merging into the system.The proposed algorithm can achieve better performance under the condition of non-Gaussian measurement noise in comparison with benchmark algorithms.The simulation results demonstrate the advantages of the proposed SLAM algorithm.展开更多
The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two c...The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted mean.Due to the wide applicability of these tools,we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.展开更多
In order to evaluate the nonlinear performance and the possible damage to rubber-bearings (RBs) during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinea...In order to evaluate the nonlinear performance and the possible damage to rubber-bearings (RBs) during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB (GZN 110) under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least- square estimation (SNLSE), is introduced to identify the model parameters. It is shown that the proposed simplified Bouc- Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.展开更多
Vehicle mass is an important parameter in vehicle dynamics control systems. Although many algorithms have been developed for the estimation of mass, none of them have yet taken into account the different types of resi...Vehicle mass is an important parameter in vehicle dynamics control systems. Although many algorithms have been developed for the estimation of mass, none of them have yet taken into account the different types of resistance that occur under different conditions. This paper proposes a vehicle mass estimator. The estimator incorporates road gradient information in the longitudinal accelerometer signal, and it removes the road grade from the longitudinal dynamics of the vehicle. Then, two different recursive least square method (RLSM) schemes are proposed to estimate the driving resistance and the mass independently based on the acceleration partition under different conditions. A 6 DOF dynamic model of four In-wheel Motor Vehicle is built to assist in the design of the algorithm and in the setting of the parameters. The acceleration limits are determined to not only reduce the estimated error but also ensure enough data for the resistance estimation and mass estimation in some critical situations. The modification of the algorithm is also discussed to improve the result of the mass estimation. Experiment data on asphalt road, plastic runway, and gravel road and on sloping roads are used to validate the estimation algorithm. The adaptability of the algorithm is improved by using data collected under several critical operating conditions. The experimental results show the error of the estimation process to be within 2.6%, which indicates that the algorithm can estimate mass with great accuracy regardless of the road surface and gradient changes and that it may be valuable in engineering applications. This paper proposes a recursive least square vehicle mass estimation method based on acceleration partition.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
The paper introduces a new biased estimator namely Generalized Optimal Estimator (GOE) in a multiple linear regression when there exists multicollinearity among predictor variables. Stochastic properties of proposed e...The paper introduces a new biased estimator namely Generalized Optimal Estimator (GOE) in a multiple linear regression when there exists multicollinearity among predictor variables. Stochastic properties of proposed estimator were derived, and the proposed estimator was compared with other existing biased estimators based on sample information in the the Scalar Mean Square Error (SMSE) criterion by using a Monte Carlo simulation study and two numerical illustrations.展开更多
This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme,...This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme, using a variable transformation of the auxiliary variable, x. All the six estimators proposed by [1] are easily identified as special cases of the proposed class of estimators. Asymptotic properties of the proposed class of estimators are derived theoretically and subsequently verified using empirical illustrations. Some of the proposed estimators are found to have relatively large gains in efficiency over the customary ratio estimator, ?for the given data set.展开更多
By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation i...By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation is considerably more intuitive, and is analytically more tractable.展开更多
In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression ...In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression model with exact linear restrictions. However, there are some situations, where the linear restrictions are stochastic. In this paper, we propose a Stochastic Restricted Maximum Likelihood Estimator (SRMLE) for the logistic regression model with stochastic linear restrictions to overcome this issue. Moreover, a Monte Carlo simulation is conducted for comparing the performances of the MLE, Restricted Maximum Likelihood Estimator (RMLE), Ridge Type Logistic Estimator(LRE), Liu Type Logistic Estimator(LLE), and SRMLE for the logistic regression model by using Scalar Mean Squared Error (SMSE).展开更多
文摘This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.
文摘In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works;(ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution;(iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Holder continuous) and pathdistribution dependent.
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The least trimmed squares estimator (LTS) is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. We show that the LTS estimate can be obtained by a simple algorithm with the complexity 0( N In N) for large N, where N is the number of measurements. We also show that though the LTS is robust in terms of the outliers, it is sensitive to the inliers. The concept of the inliers is introduced. Moreover, the Generalized Least Trimmed Squares estimator (GLTS) together with its solution are presented that reduces the effect of both the outliers and the inliers. Keywords Least squares - Least trimmed squares - Outliers - System identification - Parameter estimation - Robust parameter estimation This work was supported in part by NSF ECS — 9710297 and ECS — 0098181.
文摘It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.
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This work is supported by Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX18_0467)Jiangsu Province,China.During the revision of this paper,the author is supported by China Scholarship Council(No.201906840021)China to continue some research related to data processing.
文摘Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.
文摘Phasor Measurement Units(PMUs)provide Global Positioning System(GPS)time-stamped synchronized measurements of voltage and current with the phase angle of the system at certain points along with the grid system.Those synchronized data measurements are extracted in the form of amplitude and phase from various locations of the power grid to monitor and control the power system condition.A PMU device is a crucial part of the power equipment in terms of the cost and operative point of view.However,such ongoing development and improvement to PMUs’principal work are essential to the network operators to enhance the grid quality and the operating expenses.This paper introduces a proposed method that led to lowcost and less complex techniques to optimize the performance of PMU using Second-Order Kalman Filter.It is based on the Asyncrhophasor technique resulting in a phase error minimization when receiving the signal from an access point or from the main access point.The MATLAB model has been created to implement the proposed method in the presence of Gaussian and non-Gaussian.The results have shown the proposed method which is Second-Order Kalman Filter outperforms the existing model.The results were tested usingMean Square Error(MSE).The proposed Second-Order Kalman Filter method has been replaced with a synchronization unit into thePMUstructure to clarify the significance of the proposed new PMU.
基金Sponsored by the National Natural Science Foundation of China(Grant No.60672008)the Space Technology Innovation Foundation of China
文摘In the osmotic dehydration process of food,on-line estimation of concentrations of two components in ternary solution with NaCl and sucrose was performed based on multi-functional sensing technique.Moving Least Squares were adopted in approximation procedure to estimate the viscosity of such interested ternary solution with the given data set.As a result,in one mode of using total experimental data as calibration data and validation data,the relative deviations of estimated viscosities are less than ±1.24%.In the other mode,by taking total experimental data except the ones for estimation as calibration data,the relative deviations are less than ±3.47%.In the same way,the density of ternary solution can be also estimated with deviations less than ± 0.11% and ± 0.30% respectively in these two models.The satisfactory and accurate results show the extraordinary efficiency of Moving Least Squares behaved in signal approximation for multi-functional sensors.
基金Supported by the National High Technology Research and Development Program of China(2010AA09Z104)the Fundamental Research Funds of the Zhejiang University(2014FZA5020)
文摘Mobile robot systems performing simultaneous localization and mapping(SLAM) are generally plagued by non-Gaussian noise.To improve both accuracy and robustness under non-Gaussian measurement noise,a robust SLAM algorithm is proposed.It is based on the square-root cubature Kalman filter equipped with a Huber' s generalized maximum likelihood estimator(GM-estimator).In particular,the square-root cubature rule is applied to propagate the robot state vector and covariance matrix in the time update,the measurement update and the new landmark initialization stages of the SLAM.Moreover,gain weight matrices with respect to the measurement residuals are calculated by utilizing Huber' s technique in the measurement update step.The measurement outliers are suppressed by lower Kalman gains as merging into the system.The proposed algorithm can achieve better performance under the condition of non-Gaussian measurement noise in comparison with benchmark algorithms.The simulation results demonstrate the advantages of the proposed SLAM algorithm.
文摘The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted mean.Due to the wide applicability of these tools,we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.
基金National Natural Science Foundation of China Under Grant No.10572058the Science Foundation of Aeronautics of China Under Grant No.2008ZA52012
文摘In order to evaluate the nonlinear performance and the possible damage to rubber-bearings (RBs) during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB (GZN 110) under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least- square estimation (SNLSE), is introduced to identify the model parameters. It is shown that the proposed simplified Bouc- Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.
基金Supported by National Basic Research Program of China(Grant No.2011CB711200)
文摘Vehicle mass is an important parameter in vehicle dynamics control systems. Although many algorithms have been developed for the estimation of mass, none of them have yet taken into account the different types of resistance that occur under different conditions. This paper proposes a vehicle mass estimator. The estimator incorporates road gradient information in the longitudinal accelerometer signal, and it removes the road grade from the longitudinal dynamics of the vehicle. Then, two different recursive least square method (RLSM) schemes are proposed to estimate the driving resistance and the mass independently based on the acceleration partition under different conditions. A 6 DOF dynamic model of four In-wheel Motor Vehicle is built to assist in the design of the algorithm and in the setting of the parameters. The acceleration limits are determined to not only reduce the estimated error but also ensure enough data for the resistance estimation and mass estimation in some critical situations. The modification of the algorithm is also discussed to improve the result of the mass estimation. Experiment data on asphalt road, plastic runway, and gravel road and on sloping roads are used to validate the estimation algorithm. The adaptability of the algorithm is improved by using data collected under several critical operating conditions. The experimental results show the error of the estimation process to be within 2.6%, which indicates that the algorithm can estimate mass with great accuracy regardless of the road surface and gradient changes and that it may be valuable in engineering applications. This paper proposes a recursive least square vehicle mass estimation method based on acceleration partition.
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The paper introduces a new biased estimator namely Generalized Optimal Estimator (GOE) in a multiple linear regression when there exists multicollinearity among predictor variables. Stochastic properties of proposed estimator were derived, and the proposed estimator was compared with other existing biased estimators based on sample information in the the Scalar Mean Square Error (SMSE) criterion by using a Monte Carlo simulation study and two numerical illustrations.
文摘This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme, using a variable transformation of the auxiliary variable, x. All the six estimators proposed by [1] are easily identified as special cases of the proposed class of estimators. Asymptotic properties of the proposed class of estimators are derived theoretically and subsequently verified using empirical illustrations. Some of the proposed estimators are found to have relatively large gains in efficiency over the customary ratio estimator, ?for the given data set.
文摘By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation is considerably more intuitive, and is analytically more tractable.
文摘In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression model with exact linear restrictions. However, there are some situations, where the linear restrictions are stochastic. In this paper, we propose a Stochastic Restricted Maximum Likelihood Estimator (SRMLE) for the logistic regression model with stochastic linear restrictions to overcome this issue. Moreover, a Monte Carlo simulation is conducted for comparing the performances of the MLE, Restricted Maximum Likelihood Estimator (RMLE), Ridge Type Logistic Estimator(LRE), Liu Type Logistic Estimator(LLE), and SRMLE for the logistic regression model by using Scalar Mean Squared Error (SMSE).