This paper addresses the problem of providing robust estimators under a functional logistic regression model. Logistic regression is a popular tool in classification problems with two populations. As in functional linear regression, regularization tools are needed to compute estimators for the functional slope. The traditional methods are based on dimension reduction or penalization combined with maximum likelihood or quasi--likelihood techniques and for that reason, they may be affected by misclassified points especially if they are associated to functional covariates with atypical behaviour. The proposal given in this paper adapts some of the best practices used when the covariates are finite--dimensional to provide reliable estimations. Under regularity conditions, consistency of the resulting estimators and rates of convergence for the predictions are derived. A numerical study illustrates the finite sample performance of the proposed method and reveals its stability under different contamination scenarios. A real data example is also presented.

翻译：本文探讨了在函数型逻辑回归模型下提供稳健估计量的问题。逻辑回归是两总体分类问题中的常用工具。与函数型线性回归类似，需要借助正则化方法来计算函数型斜率的估计量。传统方法基于降维或惩罚技术，并结合极大似然或拟似然方法，因此可能受误分类点的影响，特别是当这些点与具有异常行为的函数型协变量相关时。本文提出的方案借鉴了协变量为有限维情形下的一些最佳实践，以提供可靠的估计。在正则性条件下，推导了所得估计量的一致性以及预测的收敛速率。数值研究展示了所提方法在有限样本下的表现，并揭示了其在多种污染场景下的稳定性。同时给出了一个实际数据例子。