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Semiparametric Single-index Poisson Regression Model with Unobserved Heterogeneity

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Listed:
  • 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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    References listed on IDEAS

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    1. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    2. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    3. Miguel A. Delgado & Thomas J. Kniesner, 1997. "Count Data Models With Variance Of Unknown Form: An Application To A Hedonic Model Of Worker Absenteeism," The Review of Economics and Statistics, MIT Press, vol. 79(1), pages 41-49, February.
    4. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    5. Christine Seller & John R. Stoll & Jean-Paul Chavas, 1985. "Validation of Empirical Measures of Welfare Change: A Comparison of Nonmarket Techniques," Land Economics, University of Wisconsin Press, vol. 62(2), pages 156-175.
    6. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    7. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
    8. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    9. Picone, Gabriel A. & Butler, J.S., 2000. "Semiparametric Estimation Of Multiple Equation Models," Econometric Theory, Cambridge University Press, vol. 16(4), pages 551-575, August.
    10. Newey, Whitney K & Stoker, Thomas M, 1993. "Efficiency of Weighted Average Derivative Estimators and Index Models," Econometrica, Econometric Society, vol. 61(5), pages 1199-1223, September.
    11. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    12. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(3), pages 560-586, June.
    13. Sherman, Robert P., 1994. "U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 372-395, June.
    14. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
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