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Statistical inference for multivariate partially linear regression models |
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| Authors: | Jinhong You Yong Zhou Gemai Chen |
| Affiliation: | 1. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, P.R. China;2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R. China;3. Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4;4. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, P.R. China |
| Abstract: | In this paper we study a class of multivariate partially linear regression models. Various estimators for the parametric component and the nonparametric component are constructed and their asymptotic normality established. In particular, we propose an estimator of the contemporaneous correlation among the multiple responses and develop a test for detecting the existence of such contemporaneous correlation without using any nonparametric estimation. The performance of the proposed estimators and test is evaluated through some simulation studies and an analysis of a real data set is used to illustrate the developed methodology. The Canadian Journal of Statistics 41: 1–22; 2013 © 2013 Statistical Society of Canada |
| Keywords: | Contemporaneous correlation partially linear regression profile least squares semiparametric efficiency two‐stage estimation MSC 2010: Primary 62H12 secondary 62A10 |