## Maximum L$$q$$-likelihood estimation.(English)Zbl 1183.62033

Summary: The maximum L$$q$$-likelihood estimator (ML$$q$$E), a new parameter estimator based on nonextensive entropy [J. Havrda and F. Charvat, Kybernetika 3, 30–35 (1967; Zbl 0178.22401)] 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 proper asymptotic normality and efficiency of ML$$q$$E is established.

### MSC:

 62F10 Point estimation 60F05 Central limit and other weak theorems 62B10 Statistical aspects of information-theoretic topics 62G32 Statistics of extreme values; tail inference 65C60 Computational problems in statistics (MSC2010) 62F12 Asymptotic properties of parametric estimators

Zbl 0178.22401
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### References:

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