Abstract
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.
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Acknowledgments
The research and education chair of civil engineering and eco-construction is financed by the Chamber of Trade and Industry of Nantes and Saint-Nazaire cities, the CARENE (urban agglomeration of Saint-Nazaire), Charier, Architectes Ingénieurs Associés, Vinci construction, the Regional Federation of Buildings, and the Regional Federation of Public Works. The authors wish also to thank these partners for their patronage. The authors would like to thank two anonymous referees for their careful readings and helpful comments that led to a considerable improvement of the paper.
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Senga Kiessé, T., Zougab, N. & Kokonendji, C.C. Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data. Comput Stat 31, 189–206 (2016). https://doi.org/10.1007/s00180-015-0627-1
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DOI: https://doi.org/10.1007/s00180-015-0627-1