In this paper, linear errors-in-response models are considered in the presence of validation data on the responses. A semiparametric dimension reduction technique is employed to define an estimator of β with asymptot...In this paper, linear errors-in-response models are considered in the presence of validation data on the responses. A semiparametric dimension reduction technique is employed to define an estimator of β with asymptotic normality, the estimated empirical loglikelihoods and the adjusted empirical loglikelihoods for the vector of regression coefficients and linear combinations of the regression coefficients, respectively. The estimated empirical log-likelihoods are shown to be asymptotically distributed as weighted sums of independent X 2 1 and the adjusted empirical loglikelihoods are proved to be asymptotically distributed as standard chi-squares, respectively.展开更多
This paper considers partial function linear models of the form Y =∫X(t)β(t)dt + g(T)with Y measured with error. The authors propose an estimation procedure when the basis functions are data driven, such as with fun...This paper considers partial function linear models of the form Y =∫X(t)β(t)dt + g(T)with Y measured with error. The authors propose an estimation procedure when the basis functions are data driven, such as with functional principal components. Estimators of β(t) and g(t) with the primary data and validation data are presented and some asymptotic results are given. Finite sample properties are investigated through some simulation study and a real data application.展开更多
基金This work was supported by the National Natural Science Foundation of China(Key Grant 10231030,Special Grant 10241001)Humboldt-Universitat Berlin-Sonderforschungsbereich 373.
文摘In this paper, linear errors-in-response models are considered in the presence of validation data on the responses. A semiparametric dimension reduction technique is employed to define an estimator of β with asymptotic normality, the estimated empirical loglikelihoods and the adjusted empirical loglikelihoods for the vector of regression coefficients and linear combinations of the regression coefficients, respectively. The estimated empirical log-likelihoods are shown to be asymptotically distributed as weighted sums of independent X 2 1 and the adjusted empirical loglikelihoods are proved to be asymptotically distributed as standard chi-squares, respectively.
基金supported by the National Natural Science Foundation of China under Grant Nos.11561006 and 11471127Master Foundation of Guangxi University of Technology under Grant No.070235+2 种基金Doctoral Foundation of Guangxi University of Science and Technology under Grant No.14Z07Research Projects of Colleges and Universities in Guangxi under Grant No.KY2015YB171the Open Fund Project of Guangxi Colleges and Universities Key Laboratory of Mathematics and Statistical Model under Grant No.2016GXKLMS005
文摘This paper considers partial function linear models of the form Y =∫X(t)β(t)dt + g(T)with Y measured with error. The authors propose an estimation procedure when the basis functions are data driven, such as with functional principal components. Estimators of β(t) and g(t) with the primary data and validation data are presented and some asymptotic results are given. Finite sample properties are investigated through some simulation study and a real data application.
