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Generalized weighted likelihood density estimators with application to finite mixture of exponential family distributions

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  • Zhan, Tingting
  • Chevoneva, Inna
  • Iglewicz, Boris

Abstract

The family of weighted likelihood estimators largely overlaps with minimum divergence estimators. They are robust to data contaminations compared to MLE. We define the class of generalized weighted likelihood estimators (GWLE), provide its influence function and discuss the efficiency requirements. We introduce a new truncated cubic-inverse weight, which is both first and second order efficient and more robust than previously reported weights. We also discuss new ways of selecting the smoothing bandwidth and weighted starting values for the iterative algorithm. The advantage of the truncated cubic-inverse weight is illustrated in a simulation study of three-component normal mixtures model with large overlaps and heavy contaminations. A real data example is also provided.

Suggested Citation

  • Zhan, Tingting & Chevoneva, Inna & Iglewicz, Boris, 2011. "Generalized weighted likelihood density estimators with application to finite mixture of exponential family distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 457-465, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:457-465
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    References listed on IDEAS

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    1. Ishwaran H. & James L.F. & Sun J., 2001. "Bayesian Model Selection in Finite Mixtures by Marginal Density Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1316-1332, December.
    2. 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.
    3. 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.
    4. Marianthi Markatou, 2000. "Mixture Models, Robustness, and the Weighted Likelihood Methodology," Biometrics, The International Biometric Society, vol. 56(2), pages 483-486, June.
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