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Semiparametric Single-index Poisson Regression Model with Unobserved Heterogeneity

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  • Jérôme Foncel

    (Crest)

  • Marian Hristache

    (Crest)

  • Valentin Patilea

    (Crest)

Abstract

We propose a two-step semiparametric pseudo-maximum likelihood procedure forsingle-index regression models where the conditional variance is a known function of theregression and an additional parameter. The Poisson single-index regression model withmultiplicative unobserved heterogeneity is an example of such a semiparametric model.Our procedure is based on linear exponential densities with nuisance parameter. Thenuisance parameter is estimated in a preliminary step and its estimate is used to buildthe pseudo-likelihood criterion for the second step. This pseudo-likelihood criterioncontains a nonparametric estimate of the index regression and therefore a rule forchoosing the smoothing parameter is needed. We propose an automatic and naturalrule based on the joint maximization of the pseudo-likelihood with respect to the indexparameter and the smoothing parameter. We derive the asymptotic properties of thesemiparametric estimator of the index parameter and the asymptotic behavior of our`optimal' smoothing parameter. The ¯nite sample performances of our methodologyare analyzed in a simulation experiment. An application to real data is also provided.

Suggested Citation

  • Jérôme Foncel & Marian Hristache & Valentin Patilea, 2004. "Semiparametric Single-index Poisson Regression Model with Unobserved Heterogeneity," Working Papers 2004-04, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2004-04
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