Consistency of LS estimate of simple linear EV model is studied. It is shown that under some common assumptions of the model, both weak and strong consistency of the estimate are equivalent but it is not so for quadra...Consistency of LS estimate of simple linear EV model is studied. It is shown that under some common assumptions of the model, both weak and strong consistency of the estimate are equivalent but it is not so for quadratic-mean consistency.展开更多
In this paper, a varying coefficient errors-in-variables model under longitudinal data is investigated.An empirical likelihood based bias-correction approach is proposed. It is proved that the proposed statistics are ...In this paper, a varying coefficient errors-in-variables model under longitudinal data is investigated.An empirical likelihood based bias-correction approach is proposed. It is proved that the proposed statistics are asymptotically chi-squared under some mild conditions, and hence can be used to construct the confidence regions of the parameters of interest. Finite sample performance of the proposed method is illustrated in a simulation study. The proposed methods are applied to an AIDS clinical trial dataset.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
This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X^Tβ ＋Z^Tα（T） ＋ε,ξ = X ＋ η with the identifying condition E[（ε,...This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X^Tβ ＋Z^Tα（T） ＋ε,ξ = X ＋ η with the identifying condition E[（ε,η^T）^T] =0, Cov[（ε,η^T）^T] = σ^2Ip＋1. The estimators of interested regression parameters /3 , and the model error variance σ2, as well as the nonparametric components α（T）, are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ2 are strongly consistent and asymptotically normal and that the estimator of α（T） achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the VN,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests.展开更多
The M-estimate of parameters in the errors-in-variables (EV) model Y =xτβ0+∈,X =x+u ((∈,uτ)τ is a (p+1)-dimensional spherical error, Coy[(∈, uτ)τ] =σ2Ip+1)being considered. The M-estimate βn,, of β0 under ...The M-estimate of parameters in the errors-in-variables (EV) model Y =xτβ0+∈,X =x+u ((∈,uτ)τ is a (p+1)-dimensional spherical error, Coy[(∈, uτ)τ] =σ2Ip+1)being considered. The M-estimate βn,, of β0 under a general ρ(·) function and the estimateof σ2 are given, the strong consistency and asymptotic normality of βn as well as are obtained. The conditions for the ρ(·) function in this paper are similar to that of linearexpression of M-estimates in the linear regression model.展开更多
The aim of this work is to construct the parameter estimators in the partial linear errors-in-variables (EV) models and explore their asymptotic properties. Unlike other related References, the assumption of known err...The aim of this work is to construct the parameter estimators in the partial linear errors-in-variables (EV) models and explore their asymptotic properties. Unlike other related References, the assumption of known error covariance matrix is removed when the sample can be repeatedly drawn at each designed point from the model. The estimators of interested regression parameters, and the model error variance, as well as the nonparametric function, are constructed. Under some regular conditions, all of the estimators prove strongly consistent. Meanwhile, the asymptotic normality for the estimator of regression parameter is also presented. A simulation study is reported to illustrate our asymptotic results.展开更多
In case that replicated observations are available in someexperimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved un...In case that replicated observations are available in someexperimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved under mild conditions.展开更多
It is well known that for one-dimensional normal EV regression model X = x+ u,Y =α+βx+e, where x, u, e are mutually independent normal variables and Eu=Ee=0, the regression parameters a and β are not identifiable w...It is well known that for one-dimensional normal EV regression model X = x+ u,Y =α+βx+e, where x, u, e are mutually independent normal variables and Eu=Ee=0, the regression parameters a and β are not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a and β under some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of a and β exist, and the form of the MVUE of a and β are also given.展开更多
This paper studies the linear EV model when replicate observations are made only on independent variables. We construct the estimates of regression coefficients and prove the consistency and asymptotic normality under...This paper studies the linear EV model when replicate observations are made only on independent variables. We construct the estimates of regression coefficients and prove the consistency and asymptotic normality under some proper conditions. Results obtained reveal the difference between the case where the independent and dependent variables are observed repeatedly and simultaneously and the case studied in this article.展开更多
文摘Consistency of LS estimate of simple linear EV model is studied. It is shown that under some common assumptions of the model, both weak and strong consistency of the estimate are equivalent but it is not so for quadratic-mean consistency.
基金Supported by National Social Science Foundation of China(16BTJ015)
文摘In this paper, a varying coefficient errors-in-variables model under longitudinal data is investigated.An empirical likelihood based bias-correction approach is proposed. It is proved that the proposed statistics are asymptotically chi-squared under some mild conditions, and hence can be used to construct the confidence regions of the parameters of interest. Finite sample performance of the proposed method is illustrated in a simulation study. The proposed methods are applied to an AIDS clinical trial dataset.
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.
基金Supported by the National Natural Science Foundation of China (No.40574003) the National Natural Science of Hunan (NO.03JJY3065).
文摘This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X^Tβ ＋Z^Tα（T） ＋ε,ξ = X ＋ η with the identifying condition E[（ε,η^T）^T] =0, Cov[（ε,η^T）^T] = σ^2Ip＋1. The estimators of interested regression parameters /3 , and the model error variance σ2, as well as the nonparametric components α（T）, are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ2 are strongly consistent and asymptotically normal and that the estimator of α（T） achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the VN,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests.
文摘The M-estimate of parameters in the errors-in-variables (EV) model Y =xτβ0+∈,X =x+u ((∈,uτ)τ is a (p+1)-dimensional spherical error, Coy[(∈, uτ)τ] =σ2Ip+1)being considered. The M-estimate βn,, of β0 under a general ρ(·) function and the estimateof σ2 are given, the strong consistency and asymptotic normality of βn as well as are obtained. The conditions for the ρ(·) function in this paper are similar to that of linearexpression of M-estimates in the linear regression model.
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.10071009)Research Foundation of Doctorial Programme(Grant No.20020027010)the Excellent Young Teacher Programme of the Ministry of Educatioin of China
文摘The aim of this work is to construct the parameter estimators in the partial linear errors-in-variables (EV) models and explore their asymptotic properties. Unlike other related References, the assumption of known error covariance matrix is removed when the sample can be repeatedly drawn at each designed point from the model. The estimators of interested regression parameters, and the model error variance, as well as the nonparametric function, are constructed. Under some regular conditions, all of the estimators prove strongly consistent. Meanwhile, the asymptotic normality for the estimator of regression parameter is also presented. A simulation study is reported to illustrate our asymptotic results.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19631040) .
文摘In case that replicated observations are available in someexperimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved under mild conditions.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10231030).
文摘It is well known that for one-dimensional normal EV regression model X = x+ u,Y =α+βx+e, where x, u, e are mutually independent normal variables and Eu=Ee=0, the regression parameters a and β are not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a and β under some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of a and β exist, and the form of the MVUE of a and β are also given.
基金supported by the National Natural Science Foundation of China(Grant No.10231030).
文摘This paper studies the linear EV model when replicate observations are made only on independent variables. We construct the estimates of regression coefficients and prove the consistency and asymptotic normality under some proper conditions. Results obtained reveal the difference between the case where the independent and dependent variables are observed repeatedly and simultaneously and the case studied in this article.
基金The project supported by the National Natural Science Foundation of China(11171012)the Science and Technology Project of the Faculty Adviser of Excellent PHD Degree Thesis of Beijing(20111000503)+1 种基金the Beijing Municipal Education Commission Foundation(KM201110005029)Beijing Municipal Key Disciplines(006000541212010)
