Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models

Abstract

The binary-choice regression models, such as probit and logit, are used to describe the effect of explanatory variables on a binary response variable. Typically estimated by the maximum likelihood method, estimates are very sensitive to deviations from a model, such as heteroscedasticity and data contamination. At the same time, the traditional robust (high-breakdown point) methods, such as the maximum trimmed likelihood, are not applicable because, by trimming observations, they induce nonidentification of parameter estimates. To provide a robust estimation method for binary-choice regression, we consider a maximum symmetrically trimmed likelihood estimator (MSTLE) and design a parameter-free adaptive procedure for choosing the amount of trimming. The proposed adaptive MSTLE preserves the robust properties of the original MSTLE, significantly improves the finite-sample behavior of MSTLE, and also ensures the asymptotic equivalence of the MSTLE and maximum likelihood estimator under no contamination. The results concerning the trimming identification, robust properties, and asymptotic distribution of the proposed method are accompanied by simulation experiments and an application documenting the finite-sample behavior of some existing and the proposed methods.