On robustness of maximum likelihood estimates for Poisson-lognormal models

K. S. Weems and P. J. Smith

Statistics & Probability Letters, 2004, vol. 66, issue 2, 189-196

Abstract: Mixed Poisson regression models, a class of generalized linear mixed models, are commonly used to analyze count data that exhibit overdispersion. Because inference for these models can be computationally difficult, simplifying distributional assumptions are often made. We consider an influence function representing effects of infinitesimal perturbations of the mixing distribution. This function enables us to compute Gâteaux derivatives of maximum likelihood estimates (MLEs) under perturbations of the mixing distribution for Poisson-lognormal models. Provided the first two moments exist, these MLEs are robust in the sense that their Gâteaux derivatives are bounded.

Keywords: Generalized; linear; mixed; models; Robustness; Influence; functions; Gateaux; derivatives; Maximum; likelihood; estimation (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (1)

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