The Annals of Statistics

Adapting for the Missing Link

S. Weisberg and A. H. Welsh

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 22, Number 4 (1994), 1674-1700.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325749

Digital Object Identifier
doi:10.1214/aos/1176325749

Mathematical Reviews number (MathSciNet)
MR1329165

Zentralblatt MATH identifier
0828.62059

JSTOR
links.jstor.org

Subjects
Primary: 62J12: Generalized linear models
Secondary: 62G07: Density estimation

Keywords
Generalized linear model kernel smoothing link function nonparametric regression single index models

Citation

Weisberg, S.; Welsh, A. H. Adapting for the Missing Link. Ann. Statist. 22 (1994), no. 4, 1674--1700. doi:10.1214/aos/1176325749. https://projecteuclid.org/euclid.aos/1176325749


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