标题： 功能性Cox模型的最优估计 显示英文标题

标题： Optimal Estimation for the Functional Cox Model

摘要： 功能协变量在许多医学、生物人口统计学和神经影像学研究中很常见。 本文的目的是在同时存在功能协变量和标量协变量的情况下，研究右删失数据的功能Cox模型。 我们研究了最大部分似然估计量的渐近性质，并建立了有限维估计量的渐近正态性和有效性。 在再生核希尔伯特空间的框架下，功能协变量的系数函数估计量在加权$L_2$-风险下达到了最小最大最优收敛速率。 这一最优速率由删失方案、再生核和功能协变量的协方差核共同决定。 详细讨论了估计方法的实现和光滑参数的选择。 通过模拟例子和一个实际应用来说明样本性能。 显示英文摘要

摘要： Functional covariates are common in many medical, biodemographic, and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study the asymptotic properties of the maximum partial likelihood estimator and establish the asymptotic normality and efficiency of the estimator of the finite-dimensional estimator. Under the framework of reproducing kernel Hilbert space, the estimator of the coefficient function for a functional covariate achieves the minimax optimal rate of convergence under a weighted $L_2$-risk. This optimal rate is determined jointly by the censoring scheme, the reproducing kernel and the covariance kernel of the functional covariates. Implementation of the estimation approach and the selection of the smoothing parameter are discussed in detail. The finite sample performance is illustrated by simulated examples and a real application.