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Zbl 0603.62037
Zellner, Arnold
Bayesian estimation and prediction using asymmetric loss functions. (English)
[J] J. Am. Stat. Assoc. 81, 446-451 (1986). ISSN 0162-1459; ISSN 1537-274X/e

Estimators and predictors that are optimal relative to Varian's asymmetric LINEX loss function [{\it H. R. Varian}, A Bayesian approach to real estate assessment. in: {\it 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.

MSC 2000:: *62F15 Bayesian inference
62F10 Point estimation

Keywords: Bayesian estimation; prediction; linear regression; multiparameter estimation; inadmissibility; Varian's asymmetric LINEX loss function; risk functions; Bayes risks

Citations: Zbl 0365.62114

Cited in: Zbl 1142.62013 Zbl 1083.62006 Zbl 1067.62081 Zbl 0969.62007 Zbl 0747.62012 Zbl 0651.62007

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