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December, 1994 Adapting for the Missing Link
S. Weisberg, A. H. Welsh
Ann. Statist. 22(4): 1674-1700 (December, 1994). DOI: 10.1214/aos/1176325749


We consider the fitting of generalized linear models in which the link function is assumed to be unknown, and propose the following computational method: First, estimate regression coefficients using the canonical link. Then, estimate the link via a kernel smoother, treating the direction in the predictor space determined by the regression coefficients as known. Then reestimate the direction using the estimated link and alternate between these two steps. We show that under fairly general conditions, $n^{1/2}$-consistent estimates of the direction are obtained. A small Monte Carlo study is presented.


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S. Weisberg. A. H. Welsh. "Adapting for the Missing Link." Ann. Statist. 22 (4) 1674 - 1700, December, 1994.


Published: December, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0828.62059
MathSciNet: MR1329165
Digital Object Identifier: 10.1214/aos/1176325749

Primary: 62J12
Secondary: 62G07

Keywords: generalized linear model , kernel smoothing , link function , Nonparametric regression , single index models

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 4 • December, 1994
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