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Efficient Hellinger distance estimates for semiparametric models

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  • Wu, Jingjing
  • Karunamuni, Rohana J.
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 107 (2012)
    Issue (Month): C ()
    Pages: 1-23

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    Handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:1-23

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    Related research

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

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    Cited by:
    1. Tang, Qingguo & Karunamuni, Rohana J., 2013. "Minimum distance estimation in a finite mixture regression model," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 185-204.

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