Estimation of the asymptotic variance of univariate and multivariate random fields and statistical inference
Estimation of the asymptotic variance of univariate and multivariate random fields and statistical inference
复制标题
单变量和多元随机场的渐近方差估计和统计推断
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Steland
中科院分区：
文献类型：
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作者：
Annabel Prause;A. Steland
相关随机场是一种常用的方法来模拟高维数据的依赖结构，特别是在成像中收集的数据。表征依赖程度的一个重要参数是渐近方差，它是在时间和空间域中所有自协方差的总和。特别是在基于随机场部分和的测试统计量的标准化中出现，因此测试的构建需要对其进行估计。本文针对具有任意维域的严格平稳{phi}混合随机场，并在任意维的欧几里德空间中取值，提出了该参数的相合估计，从而允许多元随机场。我们建立了一致性，给出了中心极限定理，并证明了用次抽样方法可以得到基于随机场样本自协方差的相关检验统计量的分布逼近。由于在应用中，时空相关性通常是相当局部的，因此大量的自协方差消失或可以忽略不计，我们还研究了一种阈值方法，其中忽略了小幅度的样本自协方差。大量的仿真研究表明，所提出的估计器在实践中工作良好，当用于标准化图像测试统计时，可以提供高度精确的图像测试程序。
Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance which adds up all autocovariances in the temporal and spatial domain. Especially, it arises in the standardization of test statistics based on partial sums of random fields and thus the construction of tests requires its estimation. In this paper we propose consistent estimators for this parameter for strictly stationary {phi}-mixing random fields with arbitrary dimension of the domain and taking values in a Euclidean space of arbitrary dimension, thus allowing for multivariate random fields. We establish consistency, provide cen- tral limit theorems and show that distributional approximations of related test statistics based on sample autocovariances of random fields can be obtained by the subsampling approach. As in applications the spatial-temporal correlations are often quite local, such that a large number of autocovariances vanish or are negligible, we also investigate a thresholding approach where sample autocovariances of small magnitude are omitted. Extensive simulation studies show that the proposed estimators work well in practice and, when used to standardize image test statistics, can provide highly accurate image testing procedures.