In this paper, we investigate robust parameter estimation and variable selection for binary regression models with grouped 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.

在本文中，我们研究了具有分组数据的二元回归模型的稳健参数估计和变量选择. 我们研究了基于最小距离方法的估计程序。特别是，我们采用最小 Hellinger 和最小对称卡方距离标准，并提出正则化最小距离估计器。这些估计器似乎对模型错误指定和/或潜在异常值具有一定程度的自动鲁棒性。我们表明，所提出的非惩罚和惩罚最小距离估计器在模型下是有效的，同时具有出色的鲁棒性。我们研究了它们的渐近特性，例如一致性、渐近正态性和预言特性。使用蒙特卡罗研究，我们检查了所提出的估计器的小样本和稳健性特性，并将它们与传统的似然估计器进行了比较。我们还研究了两个真实数据应用程序来说明我们的方法。数值研究表明我们程序的有限样本性能令人满意。