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 since, by trimming observations, they induce the separation of data and non-identiffication 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, signifficantly improves the finite-sample behavior of MSTLE, and additionallyfensures asymptotic efficiency of the estimator under no contamination.The results concerning the trimming identiffication, 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.

Keywords: asymptotic efficiency, binary-choice regression, breakdown point, maximum likelihood estimation, robust estimation, trimming

JEL Classification: C13, C20, C21, C22