标题： 基于采样的连续过程的趋势非参数估计 显示英文标题

标题： Nonparametric estimation of a trend based upon sampled continuous processes

摘要： 设 \( X \) 是一个由紧致区间 \([0,T]\) 指数化的二阶随机过程。假设在固定的时间点集合上观察到 \( X \) 的 \( n \) 个独立实现。在关于 \( X \) 样本路径的适度正则性假设下，当 \( n, p \to \infty \) 时，我们证明了趋势函数 \( \mu = \mathbb\{E\}X \) 在空间 \( C([0,T]) \) 中的非参数估计量的渐近正态性，并利用高斯过程理论推导出 \( \mu \) 的近似同时置信带。 显示英文摘要

摘要： Let X be a second order random process indexed by a compact interval [0,T]. Assume that n independent realizations of X are observed on a fixed grid of p time points. Under mild regularity assumptions on the sample paths of X, we show the asymptotic normality of suitable nonparametric estimators of the trend function mu = EX in the space C([0,T]) as n, p go to infinity and, using Gaussian process theory, we derive approximate simultaneous confidence bands for mu.