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Statistical inference for multivariate partially linear regression models

Authors

  • Jinhong You,

    1. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, P.R. China
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  • Yong Zhou,

    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
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  • Gemai Chen

    Corresponding author
    1. Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
    2. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, P.R. China
    • Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4.
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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

Abstract

Dans cet article, nous étudions une classe de modèles de régression multivariée partiellement linéaires. Nous développons plusieurs estimateurs des composantes paramétrique et non paramétrique et établissons leur normalité asymptotique. Nous proposons notamment un estimateur de la corrélation contemporaine parmi les réponses multiples et nous construisons un test pour détecter l'existence d'une telle corrélation sans utiliser aucune estimation non paramétrique. La performance des estimateurs et du test proposés est évaluée par le biais d'études de simulation et la méthodologie élaborée est illustrée par l'analyse d'un ensemble de données réelles. La revue canadienne de statistique 41: 1–22; 2013 © 2013 Société statistique du Canada

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