论文标题
分类的强大标量逻辑回归
A robust scalar-on-function logistic regression for classification
论文作者
论文摘要
响应是二进制结果，预测因子由随机曲线组成，已成为探索二进制结果与功能预测指标之间的线性关系的一般框架，其中响应是二进制结果。用于估计该模型的大多数方法基于最小二乘类型的估计器。但是，最小二乘估计器受到异常值的严重阻碍，导致参数估计值和错误分类的可能性增加。本文提出了一种强大的部分最小二乘法，以估计标量功能逻辑回归中的回归系数函数。由功能部分最小二乘平方分解表示的回归系数函数是通过加权似然法估计的，这使异常值在响应和预测因子中的影响降低了。该方法的估计和分类性能通过一系列蒙特卡洛实验和草莓泥数据集进行评估。从提出的方法获得的结果与现有方法进行了有利的比较。
Scalar-on-function logistic regression, where the response is a binary outcome and the predictor consists of random curves, has become a general framework to explore a linear relationship between the binary outcome and functional predictor. Most of the methods used to estimate this model are based on the least-squares type estimators. However, the least-squares estimator is seriously hindered by outliers, leading to biased parameter estimates and an increased probability of misclassification. This paper proposes a robust partial least squares method to estimate the regression coefficient function in the scalar-on-function logistic regression. The regression coefficient function represented by functional partial least squares decomposition is estimated by a weighted likelihood method, which downweighs the effect of outliers in the response and predictor. The estimation and classification performance of the proposed method is evaluated via a series of Monte Carlo experiments and a strawberry puree data set. The results obtained from the proposed method are compared favorably with existing methods.
