Schwarz Methods for Quasi-Likelihood in Generalized Linear Models

Abstract

The topic is maximum likelihood estimation in generalized linear models by an approximation using a sequence of sub-models, referred to here as blocks. More broadly, the topic is the solution of a non-linear system of equations

of the type that arises in quasi-likelihood estimation, to be solved for δ ∊ R ^m .

The Schwarz methods use a sequence of sub-models, each sub-model corresponding to a subset of the components of δ, the sub-models being patched together to yield the solution for the full model. The technique might be useful for model comparison, where the fitted values from a sub-model are used as starting values for a larger model. And we explore the use of the multiplicative Schwarz method and the damped additive Schwarz method for generalized linear model with large sample sizes. It is shown that the convergence of the proposed iterative procedures is guaranteed for canonical link functions and uncanonical link functions.

Keywords:

• Generalized linear models
• Quasi-likelihood
• Schwarz methods

Mathematics Subject Classification:

• 62J12
• 62H12
• 62G08

Acknowledgment

I am grateful for the referee' careful reading of the manuscript and many valuable suggestions.