Stein-type improved estimation of standard error under asymmetric LINEX loss function

This paper considers the estimation of standard error. More than 40 years ago, Stein[C.Stein,Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean, Ann. Institute Statist. Math. 16 (1964), pp. 155-160] proposed a classical improved estimator over the minimum risk equivariant estimator under quadratic loss. This is a textbook result. A generalization of quadratic loss is LINEX loss which considers asymmetric penalty of overestimation and underestimation. What is the corresponding version to Stein's improved estimator under LINEX loss? The problem has not been solved yet. This paper gives us an answer. Our method also applies to some other loss functions such as quadratic loss and entropy loss. © 2009 Taylor & Francis.