This article studies the estimation and statistical inference problems of semi-functional partially linear regression models when the covariates in the linear part are measured with additive error. To obtain the estim...This article studies the estimation and statistical inference problems of semi-functional partially linear regression models when the covariates in the linear part are measured with additive error. To obtain the estimation of the parametric component, a corrected profile least-squares based estimation procedure is developed. Asymptotic properties of the proposed estimators are established under some mild assumptions. To test hypothesis on the parametric part, the authors propose a novel test statistic based on the difference between the corrected residual sums of squares under the null and alternative hypotheses, and show that its limiting distribution is a weighted sum of independent standard χ12. Finally, the authors illustrate the finite sample performance of the methods with some simulation studies and a real data application.展开更多
基金supported by National Natural Science Foundation of China under Grant Nos.11571112,11501372,11571148,11471160Program of Shanghai Subject Chief Scientist(14XD1401600)+2 种基金the 111 Project of China(B14019)Project of National Social Science Fund of China(15BTJ027)Research Innovation Program for ECNU Graduates(ykc17083)
文摘This article studies the estimation and statistical inference problems of semi-functional partially linear regression models when the covariates in the linear part are measured with additive error. To obtain the estimation of the parametric component, a corrected profile least-squares based estimation procedure is developed. Asymptotic properties of the proposed estimators are established under some mild assumptions. To test hypothesis on the parametric part, the authors propose a novel test statistic based on the difference between the corrected residual sums of squares under the null and alternative hypotheses, and show that its limiting distribution is a weighted sum of independent standard χ12. Finally, the authors illustrate the finite sample performance of the methods with some simulation studies and a real data application.
