For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How ...For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.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supported by the National Natural Science Foundation of China(No.12271370)。
文摘For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.
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.
