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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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.
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.
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.
Hardle, W., and J. S. Marron. 1985. Optimal bandwidth selection in nonparametric regression function estimation. Annals of Statistics 13:1465–81.
Hastings, W. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrica 57:97–109.
Kokonendji, C. C., and T. Senga Kiessé. 2011. Discrete associated kernels method and extensions. Statistical Methodology 8 (6):497–516.
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.
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.
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.
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.
Nadaraya, E. A. 1964. On estimating regression. Theory of Probability & Its Applications 9 (1):141–42.
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.
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.
Watson, G. S. 1964. Smooth regression analysis. Sankhyā: The Indian Journal of Statistics, Series A 26 (4):358–72.
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.
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.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Djerroud, L., Zougab, N. & Adjabi, S. Bayesian approach to bandwidth selection for multivariate count regression function estimation by associated discrete kernel. J Stat Theory Pract 11, 553–572 (2017). https://doi.org/10.1080/15598608.2017.1281180
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1080/15598608.2017.1281180