Bayesian Approach in Nonparametric Count Regression with Binomial Kernel

Zougab, Nabil; Adjabi, Smaïl; Kokonendji, Célestin C.

doi:10.1080/03610918.2012.725145

Cited by 10 publications

(12 citation statements)

References 20 publications

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“…Following Zougab et al (2014a) for purely nonparametric count regression, we pursue in the same manner for the semiparametric count regression function m n,h;−i in Eq. (9).…”

Section: An Mcmc Algorithmmentioning

confidence: 99%

“…Further, this choice enables the convergence of Bayesian bandwidth estimator to zero with the same rate as that of the MISE optimal bandwidth (see Remark 2 of Sect. 2 and Zougab et al 2012Zougab et al , 2014a.…”

Section: Monte Carlo Simulation Studiesmentioning

confidence: 99%

“…These indicators have been intensively employed in the literature (see Zhang et al 2009Zhang et al , 2014Hu et al 2012, or Zougab et al 2014a). To illustrate the mixing performance of Bayesian MCMC technique, we present in Tables 3 and 4 the values of BMSE and SIF indicators.…”

Section: Mcmc Convergencementioning

confidence: 99%

“…The quantity of fat in the milk increases during the first 14 weeks and decreases thereafter, see Table 9. These data have been analyzed by Senga Kiessé and Rivoire (2011) using the discrete semiparametric regression and, Kokonendji et al (2009b) and Zougab et al (2014a) using the discrete nonparametric regression. We applied the GLM and the semiparametric binomial kernel regression estimator to approximate m for the considered average daily fat data.…”

Section: Semiparametric Binomial Kernel Regressionmentioning

confidence: 99%

“…(1) have been proposed as an alternative to cross-validation procedure for bandwidth selections but only for nonparametric estimations of pmf and crf (Zougab et al 2012(Zougab et al , 2014a. This paper pursues the latter works in semiparametric framework since the semiparametric approach is demonstrated to significantly improve the purely nonparametric modelling in many situations (Abdous et al 2012).…”

Section: Introductionmentioning

confidence: 99%

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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. B Nabil Zougab

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“…Following Zougab et al (2014a) for purely nonparametric count regression, we pursue in the same manner for the semiparametric count regression function m n,h;−i in Eq. (9).…”

Section: An Mcmc Algorithmmentioning

confidence: 99%

Section: Monte Carlo Simulation Studiesmentioning

confidence: 99%