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Binomial kernel and Bayes local bandwidth in discrete function estimation

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  • N. Zougab
  • S. Adjabi
  • C. Kokonendji

Abstract

The Bayesian approach to bandwidth selection in discrete associated kernel estimation of probability mass function is a very good alternative to the classical popular methods such as the methods which adopt the asymptotic mean integrated squared error as a criterion and the cross-validation technique. In this paper, we propose a Bayesian local approach to bandwidth selection considering the binomial kernel estimator and locally treating the bandwidth h as a random quantity with a prior distribution. The local bandwidth is estimated by the posterior mean of h. The performance of this proposed approach and that of the classical methods are compared using simulations of data generated from known discrete functions. The new method is then applied to a real count data set. The smoothing quality of the Bayes estimator is very satisfactory.

Suggested Citation

  • N. Zougab & S. Adjabi & C. Kokonendji, 2012. "Binomial kernel and Bayes local bandwidth in discrete function estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 783-795.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:783-795
    DOI: 10.1080/10485252.2012.678847
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    Citations

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    Cited by:

    1. Y. Ziane & S. Adjabi & N. Zougab, 2015. "Adaptive Bayesian bandwidth selection in asymmetric kernel density estimation for nonnegative heavy-tailed data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(8), pages 1645-1658, August.
    2. Kokonendji, Célestin C. & Varron, Davit, 2016. "Performance of discrete associated kernel estimators through the total variation distance," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 225-235.
    3. Zougab, Nabil & Adjabi, Smail & Kokonendji, Célestin C., 2014. "Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 28-38.
    4. Yasmina Ziane & Nabil Zougab & Smail Adjabi, 2018. "Birnbaum–Saunders power-exponential kernel density estimation and Bayes local bandwidth selection for nonnegative heavy tailed data," Computational Statistics, Springer, vol. 33(1), pages 299-318, March.
    5. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, vol. 4(2), pages 1-27, April.
    6. Tristan Senga Kiessé & Nabil Zougab & Célestin C. Kokonendji, 2016. "Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data," Computational Statistics, Springer, vol. 31(1), pages 189-206, March.
    7. Ziane Yasmina & Zougab Nabil & Adjabi Smail, 2021. "Body tail adaptive kernel density estimation for nonnegative heavy-tailed data," Monte Carlo Methods and Applications, De Gruyter, vol. 27(1), pages 57-69, March.
    8. Sobom M. Somé & Célestin C. Kokonendji & Nawel Belaid & Smail Adjabi & Rahma Abid, 2023. "Bayesian local bandwidths in a flexible semiparametric kernel estimation for multivariate count data with diagnostics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 843-865, September.

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