Trimmed Likelihood-based Estimation in Binary Regression Models

The binary-choice regression models such as probit and logit are typically estimated by the maximum likelihood method.To improve its robustness, various M-estimation based procedures were proposed, which however require bias corrections to achieve consistency and their resistance to outliers is relatively low.On the contrary, traditional high-breakdown point methods such as maximum trimmed likelihood are not applicable since they induce the separation of data and thus non-identification of estimates by trimming observations.We propose a new robust estimator of binary-choice models based on a maximum symmetrically trimmed likelihood estimator.It is proved to be identified and consistent, and additionally, it does not create separation in the space of explanatory variables as the existing maximum trimmed likelihood.We also discuss asymptotic and robust properties of the proposed method and compare all methods by means of Monte Carlo simulations.