Advertisement

Bayesian Variance-Stabilizing Kernel Density Estimation Using Conjugate Prior

  • K. NishidaEmail author
Article
First Online:

Kernel-type density or regression estimator does not produce a constant estimator variance over the domain. To correct this problem, K. Nishida and Y. Kanazawa (2011, 2015) proposed a variance-stabilizing (VS) local variable bandwidth for kernel regression estimators. K. Nishida (2017) proposed another strategy to construct VS local linear regression estimator using a convex combination of three skewing estimators proposed by Choi and Hall (1998). In this study, we show that variance stabilization can be accomplished by a Bayesian approach in the case of kernel density estimator using conjugate prior.

This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M.J. Brewer, “A modelling approach for bandwidth selection in kernel density estimation,” in: Proceedings in Computational Statistics 13th Symposium, COMPSTAT, Bristol, UK (1998), pp. 203–208.Google Scholar
  2. 2.
    M.J. Brewer, “A Bayesian model for local smoothing in kernel density estimation,” Stat. Comput., 10, 299–309 (2000).CrossRefGoogle Scholar
  3. 3.
    N. Belaid, S. Adjabi, N. Zougab, and C.C. Kokonendji, “Bayesian bandwidth selection in discrete multivariate associated kernel estimators for probability mass functions,” J. Korean Stat. Soc., 45, 557–567 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    S.X. Chen, “Probability density function estimation using gamma kernels,” Ann. Inst. Stat. Math., 52, 471–480 (2000).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    E. Choi and P. Hall, “On bias reduction in local linear smoothing,” Biometrika, 85, No. 2, 333–345 (1998).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    L. Djerroud, N. Zougab, and S. Adjabi, “Bayesian approach to bandwidth selection for multivariate count regression function estimation by associated discrete kernel,” J. Stat. Theor. Pract., 11, 553–572 (2017).MathSciNetCrossRefGoogle Scholar
  7. 7.
    A. Gangopadhyay and K. Cheung, “Bayesian approach to the choice of smoothing parameter in kernel density estimation,” J. Nonparametr. Stat., 14, 655–664 (2002).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    K.B. Kulasekera and W.J. Padgett, “Bayes bandwidth selection in kernel density estimation with censored data,” J. Nonparametr. Stat., 18, No. 2, 129–143 (2006).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    M.S. Lima and G.S. Atuncar, “A Bayesian method to estimate the optimal bandwidth for multivariate kernel estimator,” J. Nonparametr. Stat., 23, No. 1, 137–148 (2011).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    K. Nishida, “Skewing methods for variance-stabilizing local linear regression estimation,” arXiv:1704.04356 (2017).Google Scholar
  11. 11.
    K. Nishida and Y. Kanazawa, “Introduction to the variance-stabilizing bandwidth for the Nadaraya–Watson regression estimator,” Bull. Inform. Cybern., 43, 53–66 (2011).MathSciNetzbMATHGoogle Scholar
  12. 12.
    K. Nishida and Y. Kanazawa, “On variance-stabilizing multivariate non parametric regression estimation,” Commun. Stat. Theor. Methods, 44, No. 10, 2151–2175 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    O. Scaillet, “Density estimation using inverse and reciprocal inverse gaussian kernels,” J. Nonparametr. Stat., 16, 217–266 (2004).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    H.L. Shang, “Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density,” Comput. Stat. Data Anal., 67, 185–198 (2013).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    X. Zhang, R.D. Brooks, and M.L. King, “A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation,” J. Econom., 153, 21–32 (2009).MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    X. Zhang, M.L. King, and R.J. Hyndman, “A Bayesian approach to bandwidth selection for multivariate kernel density estimation,” Comput. Stat. Data Anal., 50, No. 11, 3009–3031 (2006).MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    X. Zhang, M.L. King, and H.L. Shang, “A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density,” Comput. Stat. Data Anal., 78, 218–234 (2014).MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Qi. Zheng, K.B. Kulasekera, and C. Gallagher, “Local adaptive smoothing in kernel regression estimation,” Stat. Probab. Lett., 80, 540–547 (2010).Google Scholar
  19. 19.
    Y. Ziane, S. Adjabi, and N. Zougab, “Adaptive Bayesian bandwidth selection in asymmetric kernel density estimation for nonnegative heavy-tailed data,” J. Appl. Stat., 42, No. 8, 1645–1658 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    N. Zougab, S. Adjabi, and C.C. Kokonendji, “Binomial kernel and Bayes local bandwidth in discrete function estimation,” J. Nonparametr. Stat., 24, No. 3, 783–795 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    N. Zougab, S. Adjabi, and C.C. Kokonendji, “Adaptive smoothing in associated kernel discrete functions estimation using Bayesian approach,” J. Stat. Comput. Simul., 83, 2219–2231 (2013).MathSciNetCrossRefGoogle Scholar
  22. 22.
    N. Zougab, S. Adjabi, and C.C. Kokonendji, “A Bayesian approach to bandwidth selection in univariate associate kernel estimation,” J. Stat. Theor. Pract., 7, 8–23 (2013).MathSciNetCrossRefGoogle Scholar
  23. 23.
    N. Zougab, S. Adjabi, and C.C. Kokonendji, “Bayesian approach in nonparametric count regression with binomial kernel,” Commun. Stat. Sim. Comput., 43, 1052–1063 (2014).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.General Education CenterHyogo University of Health SciencesKobeJapan

Personalised recommendations

Cite article

Buy options