Asymptotics of Bayesian median loss estimation

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Yu, Chi Wai¹  Clarke, Bertrand^2,3,4 

[1] Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China

[2] Univ Miami, Dept Med, Miami, FL 33136 USA

[3] Univ Miami, Dept Epidemiol & Publ Hlth, Miami, FL 33136 USA

[4] Univ Miami, Ctr Computat Sci, Miami, FL 33136 USA

关键词: Asymptotics;    Least median of squares estimator;    Least trimmed squares estimator;    Loss function;    Median;    Posterior;    Regression;   

DOI  :  10.1016/j.jmva.2010.04.013

来源: Elsevier

【 摘 要 】

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. (c) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free