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Discrete semiparametric regression models with associated kernel and applications

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  • T. Senga Kiessé
  • M. Rivoire

Abstract

This work is concerned with a semiparametric associated kernel estimator for count explanatory variables. The proposed semiparametric estimator is a multiplicative combination between a parametric model and a discrete nonparametric kernel estimator of Nadaraya–Watson type. In this semiparametric approach, the parametric model plays the role of the start function and the nonparametric kernel estimator is a correction factor of the parametric estimate. Some asymptotic properties of the discrete semiparametric kernel regression estimator are pointed out; in particular, we show its asymptotic normality and the order of the optimal bandwidth. The parametric part is illustrated by some nonlinear and generalised linear models; for the nonparametric estimator, we apply the discrete general triangular associated kernel providing bias reduction. The usefulness of the discrete semiparametric kernel regression estimator is shown on three practical examples in comparison with logistic, generalised linear and additive models.

Suggested Citation

  • T. Senga Kiessé & M. Rivoire, 2011. "Discrete semiparametric regression models with associated kernel and applications," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 927-941.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:927-941
    DOI: 10.1080/10485252.2011.583986
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    References listed on IDEAS

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    1. Carlos Martins-Filho & Santosh Mishra & Aman Ullah, 2008. "A Class of Improved Parametrically Guided Nonparametric Regression Estimators," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 542-573.
    2. Glad, Ingrid K., 1998. "A note on unconditional properties of a parametrically guided Nadaraya-Watson estimator," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 101-108, January.
    3. Kokonendji, Célestin C. & Zocchi, Silvio S., 2010. "Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1655-1662, November.
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    1. Tristan Senga Kiessé & Nabil Zougab & Célestin C. Kokonendji, 2016. "Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data," Computational Statistics, Springer, vol. 31(1), pages 189-206, March.

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