Asymptotics of Bayesian median loss estimation

Chi Wai Yu, Bertrand Clarke

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1950-1958
Number of pages9
JournalJournal of Multivariate Analysis
Issue number9
StatePublished - Oct 2010


  • Asymptotics
  • Least median of squares estimator
  • Least trimmed squares estimator
  • Loss function
  • Median
  • Posterior
  • Regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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