1. Statistical inference for multivariate partially linear regression models
- Author
-
Jinhong You, Yong Zhou, and Gemai Chen
- Subjects
Statistics and Probability ,Multivariate statistics ,Statistics ,Linear regression ,Econometrics ,Nonparametric statistics ,Statistical inference ,Asymptotic distribution ,Estimator ,Statistics, Probability and Uncertainty ,Regression ,Parametric statistics ,Mathematics - 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 Dans cet article, nous etudions une classe de modeles de regression multivariee partiellement lineaires. Nous developpons plusieurs estimateurs des composantes parametrique et non parametrique et etablissons leur normalite asymptotique. Nous proposons notamment un estimateur de la correlation contemporaine parmi les reponses multiples et nous construisons un test pour detecter l'existence d'une telle correlation sans utiliser aucune estimation non parametrique. La performance des estimateurs et du test proposes est evaluee par le biais d'etudes de simulation et la methodologie elaboree est illustree par l'analyse d'un ensemble de donnees reelles. La revue canadienne de statistique 41: 1–22; 2013 © 2013 Societe statistique du Canada
- Published
- 2013