High frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus

被引：7

作者：

Baldi, Paolo ^{[1
]}

Kerkyacharian, Gerard ^{[2
,3
]}

Marinucci, Domenico ^{[1
]}

Picard, Dominique ^{[2
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00161 Rome, Italy

[2] Lab Probabil & Modeles Aleatoires, F-75251 Paris 05, France

[3] Lab MODALX, Paris, France

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2008年 / 99卷 / 04期

关键词：

high frequency asymptotics; wavelets; random fields; Multivariate Central Limit Theorem; tests for Gaussianity and isotropy;

D O I：

10.1016/j.jmva.2007.02.002

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove a multivariate CLT for skewness and kurtosis of the wavelets coefficients of a stationary field on the torus. The results are in the framework of the fixed-domain asymptotics, i.e. we refer to observations of a single field which is sampled at higher and higher frequencies. We consider also studentized statistics for the case of an unknown correlation structure. The results are motivated by the analysis of high-frequency financial data or cosmological data sets, with a particular interest towards testing for Gaussianity and isotropy. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：606 / 636

页数：31

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