Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are sensitive to outliers, which may lead to inaccurate parameter estimates and inferior classification accuracy. We propose a robust estimation procedure for functional logistic regression, in which the observations of the functional predictor are projected onto a set of finite-dimensional subspaces via robust functional principal component analysis. This dimension-reduction step reduces the outlying effects in the functional predictor. The logistic regression coefficient is estimated using an M-type estimator based on binary response and robust principal component scores. In doing so, we provide robust estimates by minimizing the effects of outliers in the binary response and functional predictor variables. Via a series of Monte-Carlo simulations and using hand radiograph data, we examine the parameter estimation and classification accuracy for the response variable. We find that the robust procedure outperforms some existing robust and non-robust methods when outliers are present, while producing competitive results when outliers are absent. In addition, the proposed method is computationally more efficient than some existing robust alternatives.

翻译：函数逻辑回归是捕捉二元响应变量与函数预测变量之间线性关系的常用模型。然而，函数逻辑回归中用于参数估计的许多方法对异常值敏感，可能导致参数估计不准确和分类精度下降。我们提出了一种用于函数逻辑回归的稳健估计方法，其中函数预测变量的观测值通过稳健函数主成分分析投影到一组有限维子空间上。这一降维步骤减少了函数预测变量中的异常值影响。逻辑回归系数使用基于二元响应变量和稳健主成分得分的M型估计量进行估计。通过这种方式，我们通过最小化二元响应变量和函数预测变量中异常值的影响来提供稳健估计。通过一系列蒙特卡洛模拟并使用手部X光片数据，我们检验了响应变量的参数估计和分类精度。研究发现，当存在异常值时，该稳健方法优于一些现有的稳健和非稳健方法；当不存在异常值时，其表现也具有竞争力。此外，所提方法在计算效率上优于一些现有的稳健替代方法。