Bayesian Estimation and Prediction Using Asymmetric Loss Functions

Estimators and predictors that are optimal relative to Varian's asymmetric LINEX loss function are derived for a number of well-known models. Their risk functions and Bayes risks are derived and compared with those of usual estimators and predictors. It is shown that some usual estimators, for example, a scalar sample mean or a scalar least squares regression coefficient estimator, are inadmissible relative to asymmetric LINEX loss by providing alternative estimators that dominate them uniformly in terms of risk.