Model averaging for multivariate multiple regression models. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Zhu, Rong; Zou, Guohua; Zhang, Xinyu
• Is Part Of: Statistics. Volume 52:Issue 1(2018)
• Page Start: 205
• Page End: 227
• Publication Date: 2018-01-02
• Subjects: Asymptotic optimality -- Mahalanobis distance -- Mallows criterion -- model averaging -- multivariate multiple regression model; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2017.1367794
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: The theories and applications of model averaging have been developed comprehensively in the past two decades. In this paper, we consider model averaging for multivariate multiple regression models. In order to make use of the correlation information of the dependent variables sufficiently, we propose a model averaging method based on Mahalanobis distance which is related to the correlation of the dependent variables. We prove the asymptotic optimality of the resulting Mahalanobis Mallows model averaging (MMMA) estimators under certain assumptions. In the simulation study, we show that the proposed MMMA estimators compare favourably with model averaging estimators based on AIC and BIC weights and the Mallows model averaging estimators from the single dependent variable regression models. We further apply our method to the real data on urbanization rate and the proportion of non-agricultural population in ethnic minority areas of China.