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Semiparametric estimation in single index poisson regression: A practical approach


  • Climov, Daniela
  • Delecroix, Michel
  • Simar, Léopold


In a single index Poisson regression model with unknown link function, the index parameter can be root-n consistently estimated by the method of pseudo maximumum likelihood. In this paper, we study, by simulation arguments, the practical validity of the asymptotic behavior of the pseudo maximum likelihood index estimator and of some associated cross-validation bandwidths. A robust practical rule for implementing the pseudo maximum likelihood estimation method is suggested, which uses the bootstrap for estimating the variance of the index estimator and a variant of bagging for numerically stabilizing its variance. Our method gives reasonable results even for moderate sized samples thus it can be used for doing statistical inference in practical situtations. The procedure is illustrated through a real data example.

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  • Climov, Daniela & Delecroix, Michel & Simar, Léopold, 2001. "Semiparametric estimation in single index poisson regression: A practical approach," SFB 373 Discussion Papers 2001,51, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200151

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    1. Hardle, W. & Hall, P. & Ichimura, H., 1991. "Optimal smoothing in single index models," CORE Discussion Papers 1991007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Hardle, W. & Marron, J. S., 1995. "Fast and simple scatterplot smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 20(1), pages 1-17, July.
    3. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    4. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
    5. repec:crs:wpaper:9952 is not listed on IDEAS
    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. Sherman, Robert P., 1994. "U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 372-395, June.
    8. Michel Delecroix & Marian Hristache & Valentin Patilea, 1999. "Optimal Smoothing in Semiparametric Index Approximation of Regression Functions," Working Papers 99-52, Center for Research in Economics and Statistics.
    9. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
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    single index models; Poisson regression; kernel estimation; bandwidth selection; bootstrap;

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