Improved variance estimation under sub-space restriction

Abstract

For the linear regression model $y=X\beta +ϵ$, we assume that for a given positive definite scale matrix $\Sigma$, the error vector has a multivariate normal distribution and $\Sigma$ has the inverted Wishart distribution. For under an orthogonal sub-space restriction $H\beta =h$, we propose restricted unbiased, preliminary test and Stein-type estimators of variance of the error term, for when the scale of the inverse Wishart distribution is assumed to be unknown. We compare the weighted quadratic risks of the underlying estimators and propose dominance pictures for them.