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Likelihood-Based Local Polynomial Fitting for Single-Index Models

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  • Huh, J.
  • Park, B. U.
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    Abstract

    The parametric generalized linear model assumes that the conditional distribution of a response Y given a d-dimensional covariate X belongs to an exponential family and that a known transformation of the regression function is linear in X. In this paper we relax the latter assumption by considering a nonparametric function of the linear combination [beta]TX, say [eta]0([beta]TX). To estimate the coefficient vector [beta] and the nonparametric component [eta]0 we consider local polynomial fits based on kernel weighted conditional likelihoods. We then obtain an estimator of the regression function by simply replacing [beta] and [eta]0 in [eta]0([beta]TX) by these estimators. We derive the asymptotic distributions of these estimators and give the results of some numerical experiments.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 80 (2002)
    Issue (Month): 2 (February)
    Pages: 302-321

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    Handle: RePEc:eee:jmvana:v:80:y:2002:i:2:p:302-321

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    Related research

    Keywords: single-index models local polynomial kernel smoothers generalized linear models average derivatives;

    References

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    1. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
    2. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
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    Cited by:
    1. Feng, Long & Zou, Changliang & Wang, Zhaojun, 2012. "Rank-based inference for the single-index model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 535-541.
    2. Huh, Jib, 2010. "Detection of a change point based on local-likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1681-1700, August.
    3. Huh, Jib, 2012. "Nonparametric estimation of the regression function having a change point in generalized linear models," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 843-851.
    4. Park, Cheolwoo & Huh, Jib, 2013. "Statistical inference and visualization in scale-space using local likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 336-348.

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