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Stefan van Aelst, KULeuven Print
Thursday, 26 October 2017, 12:15 - 13:15

Stefan van Aelst, KULeuven

Robust Model Selection for Generalized Linear Models

Abstract : Generalized linear models (GLMs) are a popular framework to model the relation between a response and a set of covariates. Similarly as for linear models, outlying observations can have a large impact on standard inference procedures such as likelihood and quasi-likelihood methods. To reduce the effect of outliers, more robust inference methods have been proposed such as the quasi-likelihood M-estimator of Cantoni and Ronchetti (2001) or the weighted M-estimator after variance stabilizing transformation of Valdora and Yohai (2014). Robust model selection for GLMs was considered by Mueller and Welsh (2009) using a stratified bootstrap procedure. An obvious alternative for the computationally intensive stratified bootstrap is the fast robust bootstrap (FRB) introduced by Salibian-Barrera and Zamar (2002). However, a straightforward application of FRB for GLMs is not possible because it requires the expectation of the derivative of the loss function which causes problems for loss functions which are not everywhere differentiable. To avoid this issue, we propose another correction for the bootstrap approximations in the FRB procedure that is readily available. We show that the modified FRB inference is consistent. In particular, under suitable conditions the resulting bootstrap model selection criteria result in consistent model selection.

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