标题： 非参数估计函数数据的方差函数 显示英文标题

标题： Nonparametric Estimation of Variance Function for Functional Data

摘要： 本文研究了当均值函数未知时，函数型数据方差函数的非参数估计问题。 我们得到了基于残差平方的核估计量的渐近结果。 类似于有限维情况，我们的渐近结果表明未知均值函数的光滑性会影响收敛速度。 我们的模拟研究表明，基于残差的估计量比基于响应变量条件二阶矩的估计量表现更好。 显示英文摘要

摘要： This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite dimensional case, our asymptotic result shows the smoothness of the unknown mean function has an effect on the rate of convergence. Our simulaton studies demonstrate that estimator based on residuals performs much better than that based on conditional second moment of the responses.