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Constrained local likelihood estimators for semiparametric skew-normal distributions

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  • Yanyuan Ma
  • Jeffrey D. Hart

Abstract

A local likelihood estimator for a nonparametric nuisance function is proposed in the context of semiparametric skew-normal distributions. Constraints imposed on such functions result in a nonparametric estimator with a different target function for maximization from classical local likelihood estimators. The optimal asymptotic semiparametric efficiency bound on parameters of interest is achieved by using this estimator in conjunction with an estimating equation formed by summing efficient scores. A generalized profile likelihood approach is also proposed. This method has the advantage of providing a unique estimate in cases where an estimating equation has multiple solutions. Our nonparametric estimator of the nuisance function leads to an estimator of the semiparametric skew-normal density. Both the estimating equation and profile likelihood approaches are applicable to more general skew-symmetric distributions. Copyright 2007, Oxford University Press.

Suggested Citation

  • Yanyuan Ma & Jeffrey D. Hart, 2007. "Constrained local likelihood estimators for semiparametric skew-normal distributions," Biometrika, Biometrika Trust, vol. 94(1), pages 119-134.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:1:p:119-134
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    File URL: http://hdl.handle.net/10.1093/biomet/asm020
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    Cited by:

    1. Parisa Hasanalipour & Mostafa Razmkhah, 2021. "Testing skew-symmetry based on extreme ranked set sampling," Statistical Papers, Springer, vol. 62(5), pages 2311-2332, October.
    2. Cornelis J. Potgieter & Marc G. Genton, 2013. "Characteristic Function-based Semiparametric Inference for Skew-symmetric Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 471-490, September.
    3. Yanyuan Ma, 2015. "Discussion," International Statistical Review, International Statistical Institute, vol. 83(2), pages 207-211, August.
    4. Zhao, Xiaobing & Zhou, Xian, 2012. "Modeling gap times between recurrent events by marginal rate function," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 370-383.
    5. Mijeong Kim & Yanyuan Ma, 2012. "The efficiency of the second-order nonlinear least squares estimator and its extension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 751-764, August.

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