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arXiv · 1002.4533

Maximum L$q$-likelihood estimation

Davide Ferrari·Yuhong Yang
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Abstract

In this paper, the maximum L$q$-likelihood estimator (ML$q$E), a new parameter estimator based on nonextensive entropy [Kibernetika 3 (1967) 30--35] is introduced. The properties of the ML$q$E are studied via asymptotic analysis and computer simulations. The behavior of the ML$q$E 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 ML$q$E 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 ML$q$E is established.

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Davide Ferrari, Yuhong Yang. 2010-02-24. Maximum L$q$-likelihood estimation. https://doi.org/10.1214/09-aos687

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