Maximum L$q$-likelihood estimation
Abstract
In this paper, the maximum L-likelihood estimator (MLE), a new parameter estimator based on nonextensive entropy [Kibernetika 3 (1967) 30--35] is introduced. The properties of the MLE are studied via asymptotic analysis and computer simulations. The behavior of the MLE is characterized by the degree of distortion applied to the assumed model. When is properly chosen for small and moderate sample sizes, the MLE can successfully trade bias for precision, resulting in a substantial reduction of the mean squared error. When the sample size is large and tends to 1, a necessary and sufficient condition to ensure a proper asymptotic normality and efficiency of MLE is established.
Cite
@article{arxiv.1002.4533,
title = {Maximum L$q$-likelihood estimation},
author = {Davide Ferrari and Yuhong Yang},
journal= {arXiv preprint arXiv:1002.4533},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.1214/09-AOS687 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)