# zbMATH — the first resource for mathematics

Robust inference for generalized linear models with application to logistic regression. (English) Zbl 0994.62062
Summary: We consider a suitable scale adjustment of the estimating function which defines a class of robust $$M$$-estimators for generalized linear models. This leads to a robust version of the quasi-profile loglikelihood which allows us to derive robust likelihood ratio type tests for inference and model selection having the standard asymptotic behaviour. An application to logistic regression is discussed.

##### MSC:
 62J12 Generalized linear models (logistic models) 62F35 Robustness and adaptive procedures (parametric inference)
Full Text:
##### References:
 [1] Adimari, G., Ventura, L., 2001. Quasi-profile loglikelihoods for unbiased estimating equations. Ann. Inst. Statist. Math., to appear. · Zbl 1013.62019 [2] Cantoni, E., Ronchetti, E., 2001. Robust inference for generalized linear models. J. Amer. Statist. Assoc. 96, to appear. · Zbl 1072.62610 [3] Carroll, R.J.; Pederson, S., On robustness in the logistic regression model, J. roy. statist. soc., B 55, 693-706, (1993) · Zbl 0794.62021 [4] Hampel, F.R.; Ronchetti, E.M.; Rousseeuw, P.J.; Stahel, W.A., Robust statistics: the approach based on influence functions, (1986), Wiley New York · Zbl 0593.62027 [5] Heritier, S.; Ronchetti, E., Robust bounded-influence tests in general parametric models, J. amer. statist. assoc., 89, 897-904, (1994) · Zbl 0804.62037 [6] Heyde, C.C., Quasi-likelihood and its application, (1997), Springer New York · Zbl 0905.62014 [7] Künsch, H.R.; Stefanski, L.A.; Carroll, R.J., Conditionally unbiased bounded-influence estimation in general regression models, with applications to generalized linear models, J. amer. statist. assoc., 84, 460-466, (1989) · Zbl 0679.62024 [8] McCullagh, P.; Nelder, J.A., Generalized linear models, (1989), Chapman & Hall London [9] McCullagh, P.; Tibshirani, R., A simple method for the adjustment of profile likelihoods, J. roy. statist. soc., B 52, 325-344, (1990) · Zbl 0716.62039 [10] Pregibon, D., Resistant fits for some commonly used logistic models with medical applications, Biometrics, 55, 574-579, (1982) [11] Preisser, J.S.; Qaqish, B.F., Robust regression for clustered data with applications to binary regression, Biometrics, 55, 574-579, (1999) · Zbl 1059.62570 [12] Staudte, R.G.; Sheather, S.J., Robust estimation and testing, (1990), Wiley New York · Zbl 0706.62037 [13] Stefanski, L.A.; Carroll, R.J.; Ruppert, D., Optimally bounded score functions for generalized linear models with applications to logistic regression, Biometrika, 73, 413-424, (1986) · Zbl 0616.62043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.