Asymptotics of Bayesian median loss estimation |
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| Authors: | Chi Wai Yu Bertrand Clarke |
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| Institution: | a Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kongb Department of Medicine, University of Miami, 1120 NW 14th Street, Miami, FL, 33136, United Statesc Department of Epidemiology and Public Health, University of Miami, 1120 NW 14th Street, Miami, FL, 33136, United Statesd Center for Computational Sciences, University of Miami, 1120 NW 14th Street, Miami, FL, 33136, United States |
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| Abstract: | We establish the consistency, asymptotic normality, and efficiency for estimators derived by minimizing the median of a loss function in a Bayesian context. We contrast this procedure with the behavior of two Frequentist procedures, the least median of squares (LMS) and the least trimmed squares (LTS) estimators, in regression problems. The LMS estimator is the Frequentist version of our estimator, and the LTS estimator approaches a median-based estimator as the trimming approaches 50% on each side. We argue that the Bayesian median-based method is a good tradeoff between the two Frequentist estimators. |
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| Keywords: | 62F12 62F15 62J02 |
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