Efficient Hellinger distance estimates for semiparametric models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:107

Article

Wu, Jingjing²  Karunamuni, Rohana J.¹ 

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[2] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada

关键词: Minimum Hellinger distance estimators;    Semiparametric models;    Asymptotically efficient estimators;    Robust estimators;    Adaptive estimators;   

DOI  :  10.1016/j.jmva.2012.01.007

来源: Elsevier

【 摘 要 】

Minimum distance techniques have become increasingly important tools for solving statistical estimation and inference problems. In particular, the successful application of the Hellinger distance approach to fully parametric models is well known. The corresponding optimal estimators, known as minimum Hellinger distance estimators, achieve efficiency at the model density and simultaneously possess excellent robustness properties. For statistical models that are semiparametric, in that they have a potentially infinite dimensional unknown nuisance parameter, minimum distance methods have not been fully studied. In this paper, we extend the Hellinger distance approach to general semiparametric models and study minimum Hellinger distance estimators for semiparametric models. Asymptotic properties such as consistency, asymptotic normality, efficiency and adaptivity of the proposed estimators are investigated. Small sample and robustness properties of the proposed estimators are also examined using a Monte Carlo study. Two real data examples are analyzed as well. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free