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Biometrika 1986 73(2):413-424; doi:10.1093/biomet/73.2.413
© 1986 by Biometrika Trust
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Optimally hounded score functions for generalized linear models with applications to logistic regression

LEONARD A. STEFANSKI, RAYMOND J. CARROLL and DAVID RUPPERT

Department of Economic and Social Statistics, Cornell University Ithaca, New York 14853, U.S.A.
Department of Statistics, University of North Carolina Chapel Hill, North Carolina 27514, U.S.A.

We study optimally bounded score functions for estimating regression parameters in a generalized linear model. Our work extends results obtained by Krasker & Welsch (1982) for the linear model and provides a simple proof of Krasker & Welsch's first-order condition for strong optimality. The application of these results to logistic regression is studied in some detail with an example given comparing the bounded-influence estimator with maximum likelihood.

Key Words: Bounded influence • Generalized linear model • Influential point • Logistic regression • Outlier • Robustness


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