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A third-order bias corrected estimate in generalized linear models. (English) Zbl 1119.62067

Summary: G. M. Cordeiro and P. McCullagh [J. R. Stat. Soc., Ser. B 53, No. 3, 629–643(1991)] derived a second-order bias-corrected estimate, which displays smaller bias than the classical maximum likelihood estimate in generalized linear models. This estimate, although consistent, can display pronounced bias in small to moderately large samples, as shown by Monte Carlo simulations here. We obtain a simple matrix formula for the bias of order \(n^{-2}\) of this estimate, where n is the sample size, and define a third-order bias-corrected estimate in this class of models, which displays much smaller bias in small samples. In particular, some Monte Carlo simulations show that our new estimate can deliver substantial improvements in terms of bias and mean squared errors over the usual maximum likelihood estimate and Cordeiro and McCullagh’s estimate.

MSC:

62J12 Generalized linear models (logistic models)
62H12 Estimation in multivariate analysis
65C05 Monte Carlo methods

Software:

Fahrmeir; Ox
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Full Text: DOI

References:

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