IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/200151.html
   My bibliography  Save this paper

Semiparametric estimation in single index poisson regression: A practical approach

Author

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

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 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/62723/1/725386401.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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. repec:crs:wpaper:9952 is not listed on IDEAS
    5. 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.
    6. 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.
    7. 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.
    8. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Juan Carlos Escanciano & Kyungchul Song, 2007. "Asymptotically Optimal Tests for Single-Index Restrictions with a Focus on Average Partial Effects," PIER Working Paper Archive 07-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    2. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    3. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, Department of Economics and Business Economics, Aarhus University.
    4. Xia, Yingcun & Härdle, Wolfgang Karl & Linton, Oliver, 2009. "Optimal smoothing for a computationally and statistically efficient single index estimator," SFB 649 Discussion Papers 2009-028, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    6. Ichimura, Hidehiko & Lee, Sokbae, 2010. "Characterization of the asymptotic distribution of semiparametric M-estimators," Journal of Econometrics, Elsevier, vol. 159(2), pages 252-266, December.
    7. repec:hum:wpaper:sfb649dp2009-028 is not listed on IDEAS
    8. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
    9. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    10. Temel, Tugrul T., 2001. "A Nonparametric Hypothesis Test Via The Bootstrap Resampling," 2001 Annual meeting, August 5-8, Chicago, IL 20600, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    11. Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
    12. Khan, Shakeeb, 2001. "Two-stage rank estimation of quantile index models," Journal of Econometrics, Elsevier, vol. 100(2), pages 319-355, February.
    13. Chen, Songnian & Khan, Shakeeb & Tang, Xun, 2016. "Informational content of special regressors in heteroskedastic binary response models," Journal of Econometrics, Elsevier, vol. 193(1), pages 162-182.
    14. Severini, Thomas A. & Tripathi, Gautam, 2001. "A simplified approach to computing efficiency bounds in semiparametric models," Journal of Econometrics, Elsevier, vol. 102(1), pages 23-66, May.
    15. Delecroix, Michel & Härdle, Wolfgang & Hristache, Marian, 2003. "Efficient estimation in conditional single-index regression," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 213-226, August.
    16. Hoderlein, Stefan & Sherman, Robert, 2015. "Identification and estimation in a correlated random coefficients binary response model," Journal of Econometrics, Elsevier, vol. 188(1), pages 135-149.
    17. Kyungchul Song, 2009. "Efficient Estimation of Average Treatment Effects under Treatment-Based Sampling," PIER Working Paper Archive 09-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    18. Arthur Lewbel, 2000. "Asymptotic Trimming for Bounded Density Plug-in Estimators," Boston College Working Papers in Economics 479, Boston College Department of Economics, revised 30 Oct 2000.
    19. Ghysels, E. & Ng, S., 1996. "A Semi-Parametric Factor Model for Interest Rates," Cahiers de recherche 9612, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    20. Yassine Sbai Sassi, 2023. "The Ordinary Least Eigenvalues Estimator," Papers 2304.12554, arXiv.org.
    21. Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, vol. 143(1), pages 103-122, March.

    More about this item

    Keywords

    single index models; Poisson regression; kernel estimation; bandwidth selection; bootstrap;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:sfb373:200151. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sfhubde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.