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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

Citations:

Zbl 0178.22401
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References:

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