Estimation for Some Functions of Covariance Matrix for Multivariate Linear Model Under Non-Normality

• Activity Number: 194
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Tetsuto Himeno*+ and Takayuki Yamada
• Companies: Seikei University and The Institute of Statistical Mathematics
• Keywords: high dimension ; non-normal case ; covariance matrix ; estimation

Abstract

When we consider a statistical test in the high dimensional case, we often need estimators of the functions of the covariance matrix. Especially, it is needed to estimate the trace of squared covariance matrix or the square for the trace of the covariance matrix in the case of assessing a linear hypothesis for multivariate linear model in the high dimensional case (Fujikoshi et al. (2004, JJSS)) and dealing with a sphericity test (Ledoit and Wolf (2002, Ann. Statist.)). The unbiased and consistent estimators of these parameters are proposed in preceding study when the population distribution is multivariate normal. They are however not robust for the non-normal case. So we propose the estimators for some functions of covariance matrix for the multivariate liner model under the non-normal case. Through the numerical simulation, we confirmed the accuracy of the approximation of our proposed estimators.