Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data

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• 作者：Tristan Senga Kiessé ; Nabil Zougab ; Célestin C. Kokonendji
• 关键词：Count regression function ; Cross ; validation ; Discrete associated kernel ; MCMC ; Probability mass function
• 刊名：Computational Statistics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：31
• 期：1
• 页码：189-206
• 全文大小：519 KB
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• 作者单位：Tristan Senga Kiessé (1)
  Nabil Zougab (2) (3)
  Célestin C. Kokonendji (4)
  
  1. GeM UMR 6183 CNRS, Chair of Civil Engineering and Eco-construction, University of Nantes Angers Le Mans, Saint-Nazaire, France
  2. University of Tizi-Ouzou, Tizi-Ouzou, Algeria
  3. LAMOS, Univesrity of Bejaia, Bejaia, Algeria
  4. LMB UMR 6623 CNRS-UFC, University of Franche-Comté, Besançon, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Statistics
  Statistics
  Probability and Statistics in Computer Science
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1613-9658

文摘

This work takes advantage of semiparametric modelling which improves significantly in many situations the estimation accuracy of the purely nonparametric approach. Herein for semiparametric estimations of probability mass function (pmf) of count data, and an unknown count regression function (crf), the kernel used is a binomial one and the bandiwdth selection is investigated by developing Bayesian approaches. About the latter, Bayes local and global bandwidth approaches are used to establish data-driven selection procedures in semiparametric framework. From conjugate beta prior distributions of the smoothing parameter and under the squared errors loss function, Bayes estimate for pmf is obtained in closed form. This is not available for the crf which is computed by the Markov Chain Monte Carlo technique. Simulation studies demonstrate that both proposed methods perform better than the classical cross-validation procedures, in particular the smoothing quality and execution times are optimized. All applications are made on real data sets.