Estimators and predictors that are optimal relative to Varian’s asymmetric LINEX loss function [H. R. Varian
, A Bayesian approach to real estate assessment. in: S. E. Fienberg
and the author (eds.): Studies in Bayesian econometrics and statistics. (1975; Zbl 0365.62114
), pp. 195-208] 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.