ON MISSPECIFICATION OF THE COVARIANCE MATRIX IN LINEAR MODELS

Jian-Ying Rong (P. R. China) and Xu-Qing Liu (P. R. China)

Received December 23, 2007

Abstract

For the true model denoted by  with  and the misspecified model given as  with  the problem of estimating a parametric function, say  is considered. The general condition for the two best quadratic estimators for q under true and misspecified models to be equal is investigated. Moreover, we apply our main results to a linear regression model with the covariance matrix being compound symmetric and derive an anticipant conclusion.

Keywords and phrases: general linear model, robustness, misspecified model, misspecification, best quadratic unbiased estimation, compound symmetric.