标题： 独立线性过程数组的中心极限定理 显示英文标题

标题： Central Limit Theorems for arrays of decimated linear processes

摘要： 线性过程被定义为核与无限独立同分布随机变量序列之间的离散时间卷积。 我们通过引入分样本（decimation）来修改这个卷积，即相应地拉伸时间。 然后，我们建立了这类分样本过程的平方数组的中心极限定理。 这些定理用于获得特定频率下谱密度估计量的渐近行为。 另一个应用，将在其他地方讨论，涉及使用小波估计时间序列中的长记忆参数。 显示英文摘要

摘要： Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then establish central limit theorems for arrays of squares of such decimated processes. These theorems are used to obtain the asymptotic behavior of estimators of the spectral density at specific frequencies. Another application, treated elsewhere, concerns the estimation of the long-memory parameter in time-series, using wavelets.