Comparison of robust logistic regression estimators for variables with generalized extreme value distributions

Abstract

The aim of this study is to compare the performance of robust estimators in the presence of explanatory variables with Generalized Extreme Value (GEV) distributions in the logistic regression model. Existence of extreme values in the logistic regression model negatively affects the bias and effectiveness of classical Maximum Likelihood (ML) estimators. For this reason, robust estimators that are less sensitive to extreme values have been developed. Random variables with extreme values may be fit in one of specific distributions. In study, the GEV distribution family was examined and five robust estimators were compared for the Fréchet, Gumbel and Weibull distributions. To the simulation results, the CUBIF estimator is prominent according to both bias and efficiency criteria for small samples. In medium and large samples, while the MALLOWS estimator has the minimum bias, the CUBIF estimator has the best efficiency. The same results apply for different contamination ratios and different scale parameter values of the distributions. Simulation findings were supported by a meteorological real data application.