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April 2010 Maximum Lq-likelihood estimation
Davide Ferrari, Yuhong Yang
Ann. Statist. 38(2): 753-783 (April 2010). DOI: 10.1214/09-AOS687

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.

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Davide Ferrari. Yuhong Yang. "Maximum Lq-likelihood estimation." Ann. Statist. 38 (2) 753 - 783, April 2010. https://doi.org/10.1214/09-AOS687

Information

Published: April 2010
First available in Project Euclid: 19 February 2010

zbMATH: 1183.62033
MathSciNet: MR2604695
Digital Object Identifier: 10.1214/09-AOS687

Subjects:
Primary: 62F99
Secondary: 60F05 , 62G32 , 94A17

Keywords: Asymptotic efficiency , exponential family , Maximum Lq-likelihood estimation , nonextensive entropy , tail probability estimation

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 2 • April 2010
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