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.
Publié le : 2010-04-15
Classification:
Maximum Lq-likelihood estimation,
nonextensive entropy,
asymptotic efficiency,
exponential family,
tail probability estimation,
62F99,
60F05,
94A17,
62G32
@article{1266586613,
author = {Ferrari, Davide and Yang, Yuhong},
title = {Maximum Lq-likelihood estimation},
journal = {Ann. Statist.},
volume = {38},
number = {1},
year = {2010},
pages = { 753-783},
language = {en},
url = {http://dml.mathdoc.fr/item/1266586613}
}
Ferrari, Davide; Yang, Yuhong. Maximum Lq-likelihood estimation. Ann. Statist., Tome 38 (2010) no. 1, pp. 753-783. http://gdmltest.u-ga.fr/item/1266586613/