Model-robust parameter dispersions for iteratively re-weighted least squares

Abstract

Approximating a parameter estimator that is not a linear function of the regression response vector y by one that is suggests a generalization beyond the original linear model context of a class of model-robust dispersion estimates proposed by Glasbey (1988). The dispersion estimators that we propose can be applied whenever parameters are estimated by the iteratively reweighted least squares algorithm, regardless of the theoretical motivation for using this algorithm. We compare the performance of several such estimators in a robustified probit regression on overdispersed binomial data by simulation.

Keywords:

• generalized linear model
• overdispersion
• robust estimation
• weighted jackknife
• estimating standard errors