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Title: The penalized robust double exponential estimators Authors:  Jolien Ponnet - KU Leuven (Belgium) [presenting]
Pieter Segaert - KU Leuven (Belgium)
Stefan Van Aelst - University of Leuven (Belgium)
Tim Verdonck - UAntwerp, KU Leuven (Belgium)
Abstract: The family of double exponential distributions models both the mean and the dispersion as a function of covariates in the generalized linear model (GLM) framework. Since standard maximum likelihood inference is highly susceptible to the possible presence of outliers, we propose the robust double exponential (RDE) estimator. We focus on the penalized versions of the RDE estimator. First of all, we consider penalties for obtaining sparsity in high-dimensional settings. This allows us to select the most important predictors out of a large number that may even exceed the sample size. Secondly, we consider regularization penalties in the context of flexible smooth estimation via generalized additive models (GAMs). Hereby, the GLM for the mean and/or dispersion is replaced by a GAM. Simulation studies demonstrate the decent and robust performance of both penalized RDE estimators. Finally, the penalized RDE estimators are illustrated on real data sets.