Quadratic risk domination of restricted least squares estimators via Stein-ruled auxiliary constraints
This paper deals with the linear model \[ y=X\beta +u,\quad R\beta =r\quad and\quad u\sim N(0,\sigma^ 2I_ n). \] If m, the number of unrestricted parameters is at least 3, then the BLUE of \(\beta\) can be improved by a Stein-rule estimator depending on the choice of the used quadratic loss function. The Stein-rule depends on some parameter which is restricted to some interval and is subjected to optimization. Only under special situation the risk gain optimal parameter is independent of unknown parameters. However, the risk gain optimal parameter can be restricted to a finite interval. This interval can be further restricted if it is required that the risk gain difference is an isotonic function of some non-centrality parameter. Also relative risk gain is considered and here a confidence interval procedure is suggested to provide information regarding the actual magnitude of risk reduction achieved.
scientific article; zbMATH DE number 3958473