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.

函数逻辑回归是一种流行的模型，用于捕获二元响应和函数预测变量之间的线性关系。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，这可能导致参数估计不准确和分类精度较差。我们提出了一种用于函数逻辑回归的稳健估计程序，其中通过稳健的函数主成分分析将函数预测变量的观测值投影到一组有限维子空间上。这个降维步骤减少了函数预测器中的外围效应。使用基于二元响应和稳健主成分分数的 M 型估计器来估计逻辑回归系数。在此过程中，我们通过最小化二元响应和函数预测变量中异常值的影响来提供稳健的估计。通过一系列蒙特卡罗模拟并使用手部放射线照片数据，我们检查了响应变量的参数估计和分类准确性。我们发现，当存在异常值时，稳健过程优于一些现有的稳健和非稳健方法，而当不存在异常值时，会产生有竞争力的结果。此外，所提出的方法在计算上比一些现有的鲁棒替代方案更有效。