Maximum Lq-likelihood estimation
The Annals of Statistics · 2010 · Volume 38 · Issue 2
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.
Keywords
60F05, 62F99, 62G32, 94A17, Asymptotic efficiency, exponential family, Maximum Lq-likelihood estimation, nonextensive entropy, tail probability estimation
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