Empirical likelihood M‐estimation for the varying‐coefficient model with functional response
针对神经影像等函数数据中观测内依赖问题，提出基于广义经验似然的M估计方法，用于函数响应变系数模型，并建立统计推断和假设检验，模拟显示置信集覆盖概率接近名义水平。
Abstract This work is motivated by a gap in the functional data analysis literature, particularly in the context of neuroimaging, regarding the ability of functional models to robustly accommodate intra‐observation dependence. In response, we propose an M‐estimator based on generalized empirical likelihood for the varying‐coefficient model with a functional response. We develop statistical inference procedures, simultaneous confidence regions, and a global general linear hypothesis test for the model's functional coefficient. Our theoretical results establish the weak convergence of the log‐likelihood ratio process, a nonparametric version of Wilks' theorem for the log‐likelihood ratio, and asymptotic properties of the proposed estimator. Through a simulation study, we show that the proposed confidence sets have close‐to‐nominal coverage probabilities. In a real‐world application to a neuroimaging dataset, we show that mini‐mental state examination score and apolipoprotein E genotype have significant associations with fractional anisotropy, while associations with gender and age are only present at high quantile levels.