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Bayesian Estimation and Prediction Using Asymmetric Loss Functions

Arnold Zellner
Journal of the American Statistical Association
Vol. 81, No. 394 (Jun., 1986), pp. 446-451
DOI: 10.2307/2289234
Stable URL: http://www.jstor.org/stable/2289234
Page Count: 6
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Bayesian Estimation and Prediction Using Asymmetric Loss Functions
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Abstract

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.

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