COE-F-112 (November 2005)
Kubokawa, Tatsuya and Hisayuki Tsukuma,
"Estimation of Parameters in a Linear Regression Model under the Kullback-Leibler Loss"
Abstract
This paper is concerned with the simultaneous estimation of parameters of regression coefficients and error variance
in a linear regression model. Motivated from the Akaike information criterion, the expected Kullback-Leibler distance
is employed as a risk function for comparing estimators in a decision-theoretic framework. This setup gives us the
difficulty in handling the risk because an estimator of the variance is incorporated into the loss for estimating the
regression coefficients. In this situation, several estimators of the variance and the regression coefficients are
proposed and shown to improve on usual estimators used as a benchmark. Through simulation studies for the risk
behavior of estimators, it is numerically shown that a truncated estimator has more favorable risk than the usual
estimators.