Quasi‐Likelihood Regression with Multiple Indices and Smooth Link and Variance Functions
Journal
Scandinavian Journal of Statistics
Journal Volume
31
Journal Issue
3
Start Page
367-386
ISSN
0303-6898
1467-9469
Date Issued
2004-07-28
Author(s)
Hans‐Georg Müller
Abstract
A flexible semi-parametric regression model is proposed for modelling the relationship between a response and multivariate predictor variables. The proposed multiple-index model includes smooth unknown link and variance functions that are estimated non-parametrically. Data-adaptive methods for automatic smoothing parameter selection and for the choice of the number of indices M are considered. This model adapts to complex data structures and provides efficient adaptive estimation through the variance function component in the sense that the asymptotic distribution is the same as if the non-parametric components are known. We develop iterative estimation schemes, which include a constrained projection method for the case where the regression parameter vectors are mutually orthogonal. The proposed methods are illustrated with the analysis of data from a growth bioassay and a reproduction experiment with medflies. Asymptotic properties of the estimated model components are also obtained.
Subjects
Constrained estimation
Generalized linear models
Non-parametric quasi-likelihood
Projection pursuit regression
Pseudo-likelihood
Semi-parametric regression
Publisher
Wiley
Type
journal article