IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpem/0508007.html

A Bootstrap Test for Single Index Models

Author

Listed:
  • Wolfgang Haerdle

    (Humboldt-University of Berlin)

  • Enno MAMMEN

    (Ruprecht-Karls-University Heidelberg)

  • Isabel Proenca

    (ISEG-UTL)

Abstract

Single index models are frequently used in econometrics and biometrics. Logit and Probit models are special cases with fixed link functions. In this paper we consider a bootstrap specification test that detects nonparametric deviations of the link function. The bootstrap is used with the aim to find a more accurate distribution under the null than the normal approximation. We prove that the statistic and its bootstrapped version have the same asymptotic distribution. In a simulation study we show that the bootstrap is able to capture the negative bias and the skewness of the test statistic. It yields better approximations to the true critical values and consequently it has a more accurate level and superior power properties. We propose a modification of the HH statistic which reduces considerably the dependency of the test performance on the bandwidth choice. We show that the bootstrap of this modified statistic works as well.

Suggested Citation

  • Wolfgang Haerdle & Enno MAMMEN & Isabel Proenca, 2005. "A Bootstrap Test for Single Index Models," Econometrics 0508007, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0508007
    Note: Type of Document - pdf; prepared on windows; pages: 28
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0508/0508007.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Horowitz, Joel L., 1993. "Semiparametric estimation of a work-trip mode choice model," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 49-70, July.
    2. Isabel Proenca, "undated". "On the performance of the H-H Test," Statistic und Oekonometrie 9310, Humboldt Universitaet Berlin.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alan Ker & A. Tolga Ergun, 2007. "On the Revelation of Private Information in the U.S. Crop Insurance Program," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(4), pages 761-776, December.
    2. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2004. "Bootstrap Inference In Semiparametric Generalized Additive Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 265-300, April.

    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. Maria Fraga O. Martins, 2001. "Parametric and semiparametric estimation of sample selection models: an empirical application to the female labour force in Portugal," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(1), pages 23-39.
    2. Jorge Arana & Carmelo Leon, 2006. "Modelling unobserved heterogeneity in contingent valuation of health risks," Applied Economics, Taylor & Francis Journals, vol. 38(19), pages 2315-2325.
    3. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    4. Bellemare, C. & Melenberg, B. & van Soest, A.H.O., 2002. "Semi-parametric Models for Satisfaction with Income," Discussion Paper 2002-87, Tilburg University, Center for Economic Research.
    5. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    6. David Magaña Lemus, 2016. "Assessment of Price Risk on Agricultural Inventory Credit under Sparse Data Conditions," Economia y Sociedad., Universidad Michoacana de San Nicolas de Hidalgo, Facultad de Economia, issue 34, pages 106-118, Enero-Jun.
    7. D. F. Benoit & D. Van Den Poel, 2010. "Binary quantile regression: A Bayesian approach based on the asymmetric Laplace density," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 10/662, Ghent University, Faculty of Economics and Business Administration.
    8. Danilo Coelho & Helena Veiga & R?rt Veszteg, 2005. "Parametric and semiparametric estimation of sample selection models: an empirical application to the female labour force in Portugal," UFAE and IAE Working Papers 636.05, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    9. Florios, Kostas & Skouras, Spyros, 2008. "Exact computation of max weighted score estimators," Journal of Econometrics, Elsevier, vol. 146(1), pages 86-91, September.
    10. Fosgerau, Mogens, 2007. "Using nonparametrics to specify a model to measure the value of travel time," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(9), pages 842-856, November.
    11. Pedro Gozalo & Oliver Linton, 1994. "Local Nonlinear Least Squares Estimation: Using Parametric Information Nonparametrically," Cowles Foundation Discussion Papers 1075, Cowles Foundation for Research in Economics, Yale University.
    12. Lanot, Gauthier & Walker, Ian, 1998. "The union/non-union wage differential: An application of semi-parametric methods," Journal of Econometrics, Elsevier, vol. 84(2), pages 327-349, June.
    13. William Greene, 2007. "Discrete Choice Modeling," Working Papers 07-6, New York University, Leonard N. Stern School of Business, Department of Economics.
    14. Ginker, Tim & Lieberman, Offer, 2017. "Robustness of binary choice models to conditional heteroscedasticity," Economics Letters, Elsevier, vol. 150(C), pages 130-134.
    15. Bhat, Chandra R., 1998. "Analysis of travel mode and departure time choice for urban shopping trips," Transportation Research Part B: Methodological, Elsevier, vol. 32(6), pages 361-371, August.
    16. Roberto Rigobon, 2002. "Contagion: How to Measure It?," NBER Chapters, in: Preventing Currency Crises in Emerging Markets, pages 269-334, National Bureau of Economic Research, Inc.
    17. Florios, Kostas, 2018. "A hyperplanes intersection simulated annealing algorithm for maximum score estimation," Econometrics and Statistics, Elsevier, vol. 8(C), pages 37-55.
    18. Ker, Alan P. & Ergun, A. Tolga, 2003. "On The Revelation Of Asymmetric Information Of The Private Insurance Companies In The Us Crop Insurance Program," 2003 Annual meeting, July 27-30, Montreal, Canada 21898, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    19. Donato Romano & Riccardo Scarpa & Fiorenza Spalatro & Laura Viganò, 2000. "Modelling Determinants of Participation, Number of Trips and Site Choice for Outdoor Recreation in Protected Areas," Journal of Agricultural Economics, Wiley Blackwell, vol. 51(2), pages 224-238, May.
    20. Mark J. Garmaise & Tobias J. Moskowitz, 2002. "Informal Financial Networks: Theory and Evidence," NBER Working Papers 8874, National Bureau of Economic Research, Inc.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

    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:wpa:wuwpem:0508007. 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: EconWPA The email address of this maintainer does not seem to be valid anymore. Please ask EconWPA to update the entry or send us the correct address (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.