Regularized robust estimation in binary regression models

In this paper, we investigate robust parameter estimation and variable selection for binary regression models withgrouped data. We investigate estimation procedures based on the minimum-distance approach. In particular, we employ minimum Hellinger and minimum symmetric chi-squared distances criteria and propose regularized minimum-distance estimators. These estimators appear to possess a certain degree of automatic robustness against model misspecification and/or for potential outliers. We show that the proposed non-penalized and penalized minimum-distance estimators are efficient under the model and simultaneously have excellent robustness properties. We study their asymptotic properties such as consistency, asymptotic normality and oracle properties. Using Monte Carlo studies, we examine the small-sample and robustness properties of the proposed estimators and compare them with traditional likelihood estimators. We also study two real-data applications to illustrate our methods. The numerical studies indicate the satisfactory finite-sample performance of our procedures.

Automated summary

In this paper, we investigate the application of robust parameter estimation and variable selection in binary regression models. We propose regularized minimum-distance estimators based on the minimum-distance approach using minimum Hellinger and minimum symmetric chi-squared distances criteria. Our study shows that these estimators are efficient and possess excellent robustness properties under the model. Through Monte Carlo studies, we analyze the small-sample and robustness properties of the proposed estimators and compare them with traditional likelihood estimators. Two real-data applications illustrate the satisfactory performance of our methods.