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
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 andβare not identifiable without som...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 andβare not identifiable without some restriction imposed on the parameters.This paper discusses the problem of existence of unbiased estimate for a andβunder 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 andβexist,and the form of the MVUE of a andβare also given.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
This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END,for short)random variables.Some sufficient conditions to prove the strong law of large numbers for wei...This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END,for short)random variables.Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided.In particular,the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product.The results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random variables.As an application,the authors investigate the errors-in-variables(EV,for short)regression models and establish the strong consistency for the least square estimators.Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.展开更多
The FRF estimator based on the errors-in-variables(EV)model of multi-input multi-output(MIMO)system is presented to reduce the bias error of FRF HI estimator.The FRF HI estimator is influenced by the noises in the inp...The FRF estimator based on the errors-in-variables(EV)model of multi-input multi-output(MIMO)system is presented to reduce the bias error of FRF HI estimator.The FRF HI estimator is influenced by the noises in the inputs of the system and generates an under-estimation of the true FRF.The FRF estimator based on the EV model takes into account the errors in both the inputs and outputs of the system and would lead to more accurate FRF estimation.The FRF estimator based on the EV model is applied to the waveform replication on the 6-DOF(degree-of-freedom)hydraulic vibration table.The result shows that it is favorable to improve the control precision of the MIMO vibration control system.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
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
Though EV model is theoretically more appropriate for applications in which measurement errors exist, people are still more inclined to use the ordinary regression models and the traditional LS method owing to the dif...Though EV model is theoretically more appropriate for applications in which measurement errors exist, people are still more inclined to use the ordinary regression models and the traditional LS method owing to the difficulties of statistical inference and computation. So it is meaningful to study the performance of LS estimate in EV model. In this article we obtain general conditions guaranteeing the asymptotic normality of the estimates of regression coefficients in the linear EV model. It is noticeable that the result is in some way different from the corresponding result in the ordinary regression model.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 andβare not identifiable without some restriction imposed on the parameters.This paper discusses the problem of existence of unbiased estimate for a andβunder 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 andβexist,and the form of the MVUE of a andβare also given.
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.
基金supported by the National Natural Science Foundation of China under Grant Nos.11671012 and 11871072the Natural Science Foundation of Anhui Province under Grant Nos.1808085QA03,1908085QA01,1908085QA07+1 种基金the Provincial Natural Science Research Project of Anhui Colleges under Grant No.KJ2019A0003the Students Innovative Training Project of Anhui University under Grant No.201910357002。
文摘This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END,for short)random variables.Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided.In particular,the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product.The results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random variables.As an application,the authors investigate the errors-in-variables(EV,for short)regression models and establish the strong consistency for the least square estimators.Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.
基金This project is supported by Program for New Century Excellent Talents in University,China(No.NCET-04-0325).
文摘The FRF estimator based on the errors-in-variables(EV)model of multi-input multi-output(MIMO)system is presented to reduce the bias error of FRF HI estimator.The FRF HI estimator is influenced by the noises in the inputs of the system and generates an under-estimation of the true FRF.The FRF estimator based on the EV model takes into account the errors in both the inputs and outputs of the system and would lead to more accurate FRF estimation.The FRF estimator based on the EV model is applied to the waveform replication on the 6-DOF(degree-of-freedom)hydraulic vibration table.The result shows that it is favorable to improve the control precision of the MIMO vibration control system.
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.
文摘Though EV model is theoretically more appropriate for applications in which measurement errors exist, people are still more inclined to use the ordinary regression models and the traditional LS method owing to the difficulties of statistical inference and computation. So it is meaningful to study the performance of LS estimate in EV model. In this article we obtain general conditions guaranteeing the asymptotic normality of the estimates of regression coefficients in the linear EV model. It is noticeable that the result is in some way different from the corresponding result in the ordinary regression model.
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.
