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Minimum disparity estimation: Improved efficiency through inlier modification

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  • Mandal, Abhijit
  • Basu, Ayanendranath

Abstract

Inference procedures based on density based minimum distance techniques provide attractive alternatives to likelihood based methods for the statistician. The minimum disparity estimators are asymptotically efficient under the model; several members of this family also have strong robustness properties under model misspecification. Similarly, the disparity difference tests have the same asymptotic null distribution as the likelihood ratio test but are often superior than the latter in terms of robustness properties. However, many disparities put large weights on the inliers, cells with fewer data than expected under the model, which appears to be responsible for a somewhat poor efficiency of the corresponding methods in small samples. Here we consider several techniques which control the inliers without significantly affecting the robustness properties of the estimators and the corresponding tests. Extensive numerical studies involving simulated data illustrate the performance of the methods.

Suggested Citation

  • Mandal, Abhijit & Basu, Ayanendranath, 2013. "Minimum disparity estimation: Improved efficiency through inlier modification," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 71-86.
    • Handle: RePEc:eee:csdana:v:64:y:2013:i:c:p:71-86
    DOI: 10.1016/j.csda.2013.02.030
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    References listed on IDEAS

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    1. Basu, Ayanendranath & Harris, Ian R. & Basu, Srabashi, 1996. "Tests of hypotheses in discrete models based on the penalized Hellinger distance," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 367-373, May.
    2. Basu, Ayanendranath & Lindsay, Bruce G., 2004. "The iteratively reweighted estimating equation in minimum distance problems," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 105-124, March.
    3. Basu, A. & Mandal, A. & Pardo, L., 2010. "Hypothesis testing for two discrete populations based on the Hellinger distance," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 206-214, February.
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    Cited by:

    1. Paul, Subhadeep & Basu, Ayanendranath, 2015. "On second order efficient robust inference," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 187-207.

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