Likelihood-Based Local Polynomial Fitting for Single-Index Models

J. Huh and B. U. Park

Journal of Multivariate Analysis, 2002, vol. 80, issue 2, 302-321

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.

Keywords: single-index; models; local; polynomial; kernel; smoothers; generalized; linear; models; average; derivatives (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (5)

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