标题： 稳健的函数逻辑回归 显示英文标题

标题： Robust Functional Logistic Regression

摘要： 功能逻辑回归是一种流行的模型，用于捕捉二元响应和功能预测变量之间的线性关系。 然而，许多用于功能逻辑回归中参数估计的方法对异常值敏感，这可能导致不准确的参数估计和较差的分类准确性。 我们提出了一种针对功能逻辑回归的鲁棒估计过程，在该过程中，通过鲁棒的功能主成分分析将功能预测变量的观测值投影到一组有限维子空间上。 这一降维步骤减少了功能预测变量中的异常效应。 逻辑回归系数是通过基于二元响应和鲁棒主成分得分的M型估计量进行估计的。 这样，我们通过最小化二元响应和功能预测变量中的异常值的影响，提供了鲁棒估计。 通过一系列蒙特卡洛模拟和使用手部X光片数据，我们检验了响应变量的参数估计和分类准确性。 我们发现，当存在异常值时，鲁棒方法优于一些现有的鲁棒和非鲁棒方法，而在没有异常值时也能产生具有竞争力的结果。 此外，所提出的方法比一些现有的鲁棒替代方法计算上更高效。 显示英文摘要

摘要： 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.