Maximum Lq-likelihood estimation

Davide Ferrari, Yuhong Yang

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

In this paper, the maximum Lq-likelihood estimator (MLqE), a new parameter estimator based on nonextensive entropy [Kibernetika 3 (1967) 30-35] is introduced. The properties of the MLqE are studied via asymptotic analysis and computer simulations. The behavior of the MLqE is characterized by the degree of distortion q applied to the assumed model. When q is properly chosen for small and moderate sample sizes, the MLqE can successfully trade bias for precision, resulting in a substantial reduction of the mean squared error. When the sample size is large and q tends to 1, a necessary and sufficient condition to ensure a proper asymptotic normality and efficiency of MLqE is established.

Original languageEnglish (US)
Pages (from-to)753-783
Number of pages31
JournalAnnals of Statistics
Volume38
Issue number2
DOIs
StatePublished - Apr 2010

Keywords

  • Asymptotic efficiency
  • Exponential family
  • Maximum Lq-likelihood estimation
  • Nonextensive entropy
  • Tail probability estimation

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