Likelihood-Based Local Polynomial Fitting for Single-Index Models

✍ Scribed by J. Huh; B.U. Park

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 226 KB
• Volume: 80
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.2000.1984

✦ Synopsis

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 ; T X, say ' 0 ( ; T X). To estimate the coefficient vector ; and the nonparametric component ' 0 we consider local polynomial fits based on kernel weighted conditional likelihoods. We then obtain an estimator of the regression function by simply replacing ; and ' 0 in ' 0 ( ; T X) by these estimators. We derive the asymptotic distributions of these estimators and give the results of some numerical experiments.