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Semiparametric estimation in single index Poisson regression: A practical approach

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  • Daniela Climov
  • Michel Delecroix
  • Leopold Simar

Abstract

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 maximum likelihood. In this paper, we study, by simulation arguments, the practical validity of the asymptotic behaviour 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 situations. The procedure is illustrated through a real data example.

Suggested Citation

  • Daniela Climov & Michel Delecroix & Leopold Simar, 2002. "Semiparametric estimation in single index Poisson regression: A practical approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(7), pages 1047-1070.
    • Handle: RePEc:taf:japsta:v:29:y:2002:i:7:p:1047-1070
    DOI: 10.1080/0266476022000006739
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    References listed on IDEAS

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    1. Hardle, W. & Hall, P. & Ichimura, H., 1991. "Optimal smoothing in single index models," LIDAM Discussion Papers CORE 1991007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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.
    3. Hardle, W. & Marron, J. S., 1995. "Fast and simple scatterplot smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 20(1), pages 1-17, July.
    4. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    5. 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.
    6. 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.
    7. 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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    Cited by:

    1. Liu, Jianxuan, 2025. "Sufficient Dimension Reduction for Poisson Regression," Econometrics and Statistics, Elsevier, vol. 34(C), pages 109-119.

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