We investigate the consistency and asymptotic normality of nearest-neighbor density estimator of a sample data process based on α-mixing assumption. We extend the correspondent result under independent identical cases.
This paper based on the essay [1], studies in case that replicated observations are available in some experimental points., the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptot...This paper based on the essay [1], studies in case that replicated observations are available in some experimental points., the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptotic normality is established.展开更多
The generalized linear model(GLM) based on the observed data with incomplete information in the case of random censorship is defined. Under the given conditions, the existence and uniqueness of the solution on the l...The generalized linear model(GLM) based on the observed data with incomplete information in the case of random censorship is defined. Under the given conditions, the existence and uniqueness of the solution on the likelihood equations with respect to the parameter vector β of the model are discussed, and the consistency and asymptotic normality of the maximum likelihood estimator(MLE) βn^-, are proved.展开更多
The following heteroscedastic regression model Yi = g(xi) +σiei (1 ≤i ≤ n) is 2 considered, where it is assumed that σi^2 = f(ui), the design points (xi,ui) are known and nonrandom, g and f are unknown f...The following heteroscedastic regression model Yi = g(xi) +σiei (1 ≤i ≤ n) is 2 considered, where it is assumed that σi^2 = f(ui), the design points (xi,ui) are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.展开更多
We study the quasi likelihood equation in Generalized Linear Models(GLM) with adaptive design ∑(i=1)^n xi(yi-h(x'iβ))=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, i...We study the quasi likelihood equation in Generalized Linear Models(GLM) with adaptive design ∑(i=1)^n xi(yi-h(x'iβ))=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is shown that the Quasi- Likelihood equation for the GLM has a solution which is asymptotic normal.展开更多
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
This paper obtains asymptotic normality for double array sum of linear time series zeta(t), and gives its application in the regression model. This generalizes the main results in [1].
In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be est...In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.展开更多
Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobse...Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator for the asymptotic variance of βn(βn) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for,En, and obtain the convergest rates for En and the strong uniform convergent rates for gn(gn).展开更多
In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establi...In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.展开更多
The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint ...The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint conditional probability density function. The maximum likelihood technique is employed for obtaining the parameter estimators and the explicit expressions of the estimation error are given. The strong consistency properties of the estimators are proved by using the law of large numbers for martingales and the strong law of large numbers. The asymptotic normality of the estimation error for the diffusion parameter is obtained with the help of the strong law of large numbers and central-limit theorem. The simulation for the absolute error between estimators and true values is given and the hypothesis testing is made to verify the effectiveness of the estimators.展开更多
Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul (t), under some mild conditions the recursi...Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul (t), under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.展开更多
Let Y_i=M(X_i)+ei, where M(x)=E(Y|X=x) is an unknown realfunction on B(? R), {(X_1,Y_i)} is a stationary and m(n)-dependent sample from(X, Y), the residuals {e_i} are independent of {X_i} and have unknown common densi...Let Y_i=M(X_i)+ei, where M(x)=E(Y|X=x) is an unknown realfunction on B(? R), {(X_1,Y_i)} is a stationary and m(n)-dependent sample from(X, Y), the residuals {e_i} are independent of {X_i} and have unknown common densityf(x). In [2] a nonparametric estimate f_n(x) for f(x) has been proposed on the basisof the residuals estimates. In this paper, we further obtain the asymptotic normalityand the law of the iterated logarithm of f_n(x) under some suitable conditions. Theseresults together with those in [2] bring the asymptotic theory for the residuals densityestimate in nonparametric regression under m(n)-dependent sample to completion.展开更多
The nonparametric estimation of the next failure time is considered in this paper. The estimator given in the paper has a.s. convergence under some proper conditions. The asymptotic normality of the estimator is also ...The nonparametric estimation of the next failure time is considered in this paper. The estimator given in the paper has a.s. convergence under some proper conditions. The asymptotic normality of the estimator is also discussed.展开更多
In this paper, A nonparametric hazard estimator is introduced. Weak convergence and strong uniformly consistency of the proposed estimator lambda(n)(t) are investigated on a bounded interval, respectively. An asymptot...In this paper, A nonparametric hazard estimator is introduced. Weak convergence and strong uniformly consistency of the proposed estimator lambda(n)(t) are investigated on a bounded interval, respectively. An asymptotic representation of lambda(n)(t) is also given, and the asymptotic representation is used to prove asymptotic normality of the hazard estimator.展开更多
The assumption of homoscedasticity has received much attention in classical analysis of regression. Heteroscedasticity tests have been well studied in parametric and nonparametric regressions. The aim of this paper is...The assumption of homoscedasticity has received much attention in classical analysis of regression. Heteroscedasticity tests have been well studied in parametric and nonparametric regressions. The aim of this paper is to present a test of heteroscedasticity for nonlinear semiparametric regression models with nonparametric variance function. The validity of the proposed test is illustrated by two simulated examples and a real data example.展开更多
A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error ...A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied.展开更多
This paper proposes a new kind of generalized Friendman's urn model,which with adaptive nonhomogeneous generating matrix.This model may be applied in sequential medical experiment.In this model some limit theorems...This paper proposes a new kind of generalized Friendman's urn model,which with adaptive nonhomogeneous generating matrix.This model may be applied in sequential medical experiment.In this model some limit theorems (strong consistency and asymptot- ical normality) have been obtained.展开更多
In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function ...In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function and the properties of the estimator by using methods of numerical modeling are discussed. In the model under consideration, the estimates were compared using numerical methods to determine which of the estimates is actually better.展开更多
Once invertibility for a causal TARMA series is defined and accompanied by conditions on the probability parameters of the model, all focus concentrates on the maximum likelihood estimators. Under the coexistence of e...Once invertibility for a causal TARMA series is defined and accompanied by conditions on the probability parameters of the model, all focus concentrates on the maximum likelihood estimators. Under the coexistence of essential causality and invertibility, the estimators are shown to be convergent to the real values and asymptotically obedient to the Gaussian distribution: their variance matrix identifies with a classic result. Some real-like examples are simulated and simplification attempts include the derivation of the non-parametric chi-square test extension for stationary TAR series.展开更多
基金Sponsored by the National Natural Science Foundation of China 10771163
文摘We investigate the consistency and asymptotic normality of nearest-neighbor density estimator of a sample data process based on α-mixing assumption. We extend the correspondent result under independent identical cases.
基金the National Natural Science Foundation of China (Grant No. 19631040)
文摘This paper based on the essay [1], studies in case that replicated observations are available in some experimental points., the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptotic normality is established.
文摘The generalized linear model(GLM) based on the observed data with incomplete information in the case of random censorship is defined. Under the given conditions, the existence and uniqueness of the solution on the likelihood equations with respect to the parameter vector β of the model are discussed, and the consistency and asymptotic normality of the maximum likelihood estimator(MLE) βn^-, are proved.
基金Partially supported by the National Natural Science Foundation of China(10571136)
文摘The following heteroscedastic regression model Yi = g(xi) +σiei (1 ≤i ≤ n) is 2 considered, where it is assumed that σi^2 = f(ui), the design points (xi,ui) are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.
文摘We study the quasi likelihood equation in Generalized Linear Models(GLM) with adaptive design ∑(i=1)^n xi(yi-h(x'iβ))=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is shown that the Quasi- Likelihood equation for the GLM has a solution which is asymptotic normal.
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
基金the National Natural ScienceFoundation of China(19971001)
文摘This paper obtains asymptotic normality for double array sum of linear time series zeta(t), and gives its application in the regression model. This generalizes the main results in [1].
基金Supported by the National Natural Science Foundation of China (10571008)the Natural Science Foundation of Henan (092300410149)the Core Teacher Foundationof Henan (2006141)
文摘In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.
文摘Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator for the asymptotic variance of βn(βn) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for,En, and obtain the convergest rates for En and the strong uniform convergent rates for gn(gn).
基金supported by the Natural Science Foundation of China(10771017,10971015,10231030)Key Project to Ministry of Education of the People’s Republic of China(309007)
文摘In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.
基金National Nature Science Foundation of China(No.60974030)the Chinese Universities Scientific Fund(No.CUSF-DH-D-2014059)
文摘The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint conditional probability density function. The maximum likelihood technique is employed for obtaining the parameter estimators and the explicit expressions of the estimation error are given. The strong consistency properties of the estimators are proved by using the law of large numbers for martingales and the strong law of large numbers. The asymptotic normality of the estimation error for the diffusion parameter is obtained with the help of the strong law of large numbers and central-limit theorem. The simulation for the absolute error between estimators and true values is given and the hypothesis testing is made to verify the effectiveness of the estimators.
基金supported by the Natural Sciences and Engineering Research Council of Canadathe National Natural Science Foundation of China+2 种基金the Doctorial Fund of Education Ministry of Chinasupported by the Natural Sciences and Engineering Research Council of Canadasupported by the National Natural Science Foundation of China
文摘Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul (t), under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.
基金Project Supported by National Natural Science Foundation of China.
文摘Let Y_i=M(X_i)+ei, where M(x)=E(Y|X=x) is an unknown realfunction on B(? R), {(X_1,Y_i)} is a stationary and m(n)-dependent sample from(X, Y), the residuals {e_i} are independent of {X_i} and have unknown common densityf(x). In [2] a nonparametric estimate f_n(x) for f(x) has been proposed on the basisof the residuals estimates. In this paper, we further obtain the asymptotic normalityand the law of the iterated logarithm of f_n(x) under some suitable conditions. Theseresults together with those in [2] bring the asymptotic theory for the residuals densityestimate in nonparametric regression under m(n)-dependent sample to completion.
文摘The nonparametric estimation of the next failure time is considered in this paper. The estimator given in the paper has a.s. convergence under some proper conditions. The asymptotic normality of the estimator is also discussed.
文摘In this paper, A nonparametric hazard estimator is introduced. Weak convergence and strong uniformly consistency of the proposed estimator lambda(n)(t) are investigated on a bounded interval, respectively. An asymptotic representation of lambda(n)(t) is also given, and the asymptotic representation is used to prove asymptotic normality of the hazard estimator.
基金Supported by the Natural Science Foundation of Jiangsu Province (BK2008284)
文摘The assumption of homoscedasticity has received much attention in classical analysis of regression. Heteroscedasticity tests have been well studied in parametric and nonparametric regressions. The aim of this paper is to present a test of heteroscedasticity for nonlinear semiparametric regression models with nonparametric variance function. The validity of the proposed test is illustrated by two simulated examples and a real data example.
文摘A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied.
基金This work is supported by a grant of National University of Singapore(RP 3972712)by partially National Science Foundation of
文摘This paper proposes a new kind of generalized Friendman's urn model,which with adaptive nonhomogeneous generating matrix.This model may be applied in sequential medical experiment.In this model some limit theorems (strong consistency and asymptot- ical normality) have been obtained.
文摘In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function and the properties of the estimator by using methods of numerical modeling are discussed. In the model under consideration, the estimates were compared using numerical methods to determine which of the estimates is actually better.
文摘Once invertibility for a causal TARMA series is defined and accompanied by conditions on the probability parameters of the model, all focus concentrates on the maximum likelihood estimators. Under the coexistence of essential causality and invertibility, the estimators are shown to be convergent to the real values and asymptotically obedient to the Gaussian distribution: their variance matrix identifies with a classic result. Some real-like examples are simulated and simplification attempts include the derivation of the non-parametric chi-square test extension for stationary TAR series.