Advertisement

Journal of Statistical Theory and Practice

, Volume 11, Issue 4, pp 553–572 | Cite as

Bayesian approach to bandwidth selection for multivariate count regression function estimation by associated discrete kernel

Article

Abstract

Nonparametric regression is an important tool for exploring the unknown relationship between a response variable and a set of explanatory variables also known as regressors. This article introduces the associated discrete kernel for multivariate nonparametric count regression estimation. We propose a Bayesian approach based upon likelihood cross-validation and a Monte Carlo Markov chain (MCMC) method for deriving the global optimal bandwidths. Through simulation and real count data, we point out the performance of binomial and triangular discrete kernels. A comparative study of the Bayesian approach and cross-validation technique is also presented.

Keywords

Bayesian approach discrete kernel multivariate kernel regression cross-validation 

AMS Subject Classification

62G07 62G99 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdous, B., C. C. Kokonendji, and T. Senga Kiessé. 2012. On semiparametric regression for count explanatory variables. Journal of Statistical Planning and Inference 142:1537–48.MathSciNetCrossRefGoogle Scholar
  2. Belaid, N., S. Adjabi, N. Zougab, and C. C. Kokonendji. 2016. Bayesian bandwidth selection in discrete multivariate associated kernel estimators for probability mass functions. Journal of the Korean Statistical Society 45:557–67.MathSciNetCrossRefGoogle Scholar
  3. Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin. 2003. Bayesian data analysis, 2nd ed. Boca Raton, FL: Chapman et Hall/CRC Texts in Statistical Science.MATHGoogle Scholar
  4. Hardle, W., and J. S. Marron. 1985. Optimal bandwidth selection in nonparametric regression function estimation. Annals of Statistics 13:1465–81.MathSciNetCrossRefGoogle Scholar
  5. Hastings, W. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrica 57:97–109.MathSciNetCrossRefGoogle Scholar
  6. Kokonendji, C. C., and T. Senga Kiessé. 2011. Discrete associated kernels method and extensions. Statistical Methodology 8 (6):497–516.MathSciNetCrossRefGoogle Scholar
  7. Kokonendji, C. C., and S. S. Zocchi. 2010. Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions. Statistics and Probability Letters 80:1655–62.MathSciNetCrossRefGoogle Scholar
  8. Kokonendji, C. C., T. Senga Kiessé, and S. S. Zocchi. 2007. Discrete triangular distributions and non-parametric estimation for probability mass function. Journal of Nonparametric Statistics 19:241–54.MathSciNetCrossRefGoogle Scholar
  9. Kokonendji, C. C., T. Senga Kiessé, and C. G. Demétrio. 2009. Appropriate kernel regression on a count explanatory variable and applications. Advances and Applications in Statistics 12 (1):99–125.MathSciNetMATHGoogle Scholar
  10. Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A H. Teller, and E. Teller. 1953. Equations of state calculations by fast computing machine. Journal of Chemical Physics 21:1087–93.CrossRefGoogle Scholar
  11. Nadaraya, E. A. 1964. On estimating regression. Theory of Probability & Its Applications 9 (1):141–42.CrossRefGoogle Scholar
  12. Senga Kiessé, T., N. Zougab, and C. C. Kokonendji. 2016. Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data. Computational Statistics 31:189–206.MathSciNetCrossRefGoogle Scholar
  13. Somé, S. M., and C. C. Kokonendji. 2015. Effects of associated kernels in nonparametric multiple regressions. Journal of Statistical Theory and Practice 10 (2):456–71.MathSciNetCrossRefGoogle Scholar
  14. Watson, G. S. 1964. Smooth regression analysis. Sankhyā: The Indian Journal of Statistics, Series A 26 (4):358–72.MathSciNetGoogle Scholar
  15. Zhang, X., M. L. King, and R. J. Hyndman. 2006. A Bayesian approach to bandwidth selection for multivariate kernel density estimation. Computational Statistics and Data Analysis 50 (11):3009–31.MathSciNetCrossRefGoogle Scholar
  16. Zhang, X., R D. Brooks, and M L. King. 2009. A bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation. Journal of Econometrics 153:21–32.MathSciNetCrossRefGoogle Scholar
  17. Zhang, X., M. L. King, and H. L. Shang. 2014. A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density. Computational Statistics and Data Analysis 78:218–34.MathSciNetCrossRefGoogle Scholar
  18. Zhang, X., M. L. King, and H. L. Shang. 2016. Bayesian bandwidth selection for a nonparametric regression model with mixed types of regressors. Econometrics 4 (2):24. doi:10.3390/econometrics4020024.CrossRefGoogle Scholar
  19. Zougab, N., S. Adjabi, and C. C. Kokonendji. 2013. Bayesian approach in nonparametric count regression with binomial kernel. Communications in Statistics 43 (5):1052–63.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing, 20 Middlefield Ct, Greensboro, NC 27455 2017

Authors and Affiliations

  1. 1.LAMOS LaboratoryUniversity of BejaiaBejaiaAlgeria
  2. 2.Department of Mathematics, Faculty of SciencesUniversity of Tizi-OuzouTizi-OuzouAlgeria

Personalised recommendations