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Efficient Hellinger distance estimates for semiparametric models

  • Wu, Jingjing
  • Karunamuni, Rohana J.
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    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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    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12000085
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    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
    DOI: 10.1016/j.jmva.2012.01.007
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    1. Ayanendranath Basu & Bruce Lindsay, 1994. "Minimum disparity estimation for continuous models: Efficiency, distributions and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 683-705, December.
    2. Sriram, T. N. & Vidyashankar, A. N., 2000. "Minimum Hellinger distance estimation for supercritical Galton-Watson processes," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 331-342, December.
    3. Zudi Lu & Yer Van Hui & Andy H. Lee, 2003. "Minimum Hellinger Distance Estimation for Finite Mixtures of Poisson Regression Models and Its Applications," Biometrics, The International Biometric Society, vol. 59(4), pages 1016-1026, December.
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    6. Karlis, Dimitris & Xekalaki, Evdokia, 1998. "Minimum Hellinger distance estimation for Poisson mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 29(1), pages 81-103, November.
    7. Takada, Teruko, 2009. "Simulated minimum Hellinger distance estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2390-2403, April.
    8. Woo, Mi-Ja & Sriram, T.N., 2007. "Robust estimation of mixture complexity for count data," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4379-4392, May.
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