Robust polytomous logistic regression
针对多分类回归中异常协变量比误分类影响更大的问题，提出了两种新稳健估计量及其检验方法，通过理论、模拟和医疗数据验证其有效性。
In the context of polytomous regression, as with any generalized linear model, robustness issues are well documented. Existing robust estimators are designed to protect against misclassification, but do not protect against outlying covariates. It is shown that this can have a much bigger impact on estimation and testing than misclassification alone. To address this problem, two new estimators are introduced: a robust generalized linear model-type estimator and an optimal B-robust estimator, together with the corresponding Wald-type and score-type tests. Asymptotic distributions and variances of these estimators are provided as well as the asymptotic distributions of the test statistics under the null hypothesis. A complete comparison of the proposed new estimators and existing alternatives is presented. This is performed theoretically by studying the influence functions of the estimators, and empirically through simulations and applications to a medical dataset.