Tang Qingguo, Karunamuni Rohana J, Liu Boxiao
School of Economics and Management, Nanjing University of Science and Technology, Nanjing, People's Republic of China.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada.
J Appl Stat. 2020 Sep 18;49(3):574-598. doi: 10.1080/02664763.2020.1822304. eCollection 2022.
In this paper, we investigate robust parameter estimation and variable selection for binary regression models with . 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[具体条件未给出]的二元回归模型的稳健参数估计和变量选择。我们研究基于最小距离方法的估计程序。特别地，我们采用最小赫林格距离和最小对称卡方距离准则，并提出正则化最小距离估计量。这些估计量似乎对模型误设和/或潜在异常值具有一定程度的自动稳健性。我们表明，所提出的非惩罚和惩罚最小距离估计量在模型下是有效的，同时具有出色的稳健性。我们研究它们的渐近性质，如一致性、渐近正态性和神谕性质。通过蒙特卡罗研究，我们检验了所提出估计量的小样本和稳健性，并将它们与传统似然估计量进行比较。我们还研究了两个实际数据应用以说明我们的方法。数值研究表明我们的程序具有令人满意的有限样本性能。
