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Two generalized nonparametric methods for estimating like densities

Author

Listed:
  • Zongyuan Shang

    (University of Guelph)

  • Alan Ker

    (University of Guelph)

Abstract

This article presents two generalized nonparametric methods for estimating multiple, possibly like, densities. The first generalization contains the Nadaraya–Watson estimator, the Jones et al. (Biometrika 82(2):327–338, 1995) bias reduction estimator, and Ker (Stat Probab Lett 117:23–30, 2016) possibly similar estimator as special cases. The second generalization contains the Nadaraya–Watson estimator, Ker (2016) possibly similar estimator, and the conditional density estimator of Hall et al. (J Am Stat Assoc 99(468):1015–1026, 2004) as special cases. The generalizations do not require knowledge of the form or extent of likeness between the unknown densities; an attractive feature in empirical applications. Numerical simulations demonstrate that the two proposed generalizations lead to significant efficiency gains.

Suggested Citation

  • Zongyuan Shang & Alan Ker, 2021. "Two generalized nonparametric methods for estimating like densities," Computational Statistics, Springer, vol. 36(1), pages 113-126, March.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:1:d:10.1007_s00180-020-01007-w
    DOI: 10.1007/s00180-020-01007-w
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    References listed on IDEAS

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    1. Racine, Jeffrey S. & Ker, Alan P., 2006. "Rating Crop Insurance Policies with Efficient Nonparametric Estimators that Admit Mixed Data Types," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 31(01), pages 1-13, April.
    2. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    3. Ker, Alan P. & Ergün, A.T., 2005. "Empirical Bayes nonparametric kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 75(4), pages 315-324, December.
    4. Ker, Alan P., 2016. "Nonparametric estimation of possibly similar densities," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 23-30.
    5. Alan P. Ker & Yong Liu, 2017. "Bayesian model averaging of possibly similar nonparametric densities," Computational Statistics, Springer, vol. 32(1), pages 349-365, March.
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