环面上高斯性和各向同性小波检验的高频渐近性
High Frequency Asymptotics for Wavelet-Based Tests for Gaussianity and Isotropy on the Torus
摘要：
我们证明了一个CLT的偏度和峰度的小波系数的一个平稳域上的环面。结果是在固定域渐近的框架内，即我们指的是在越来越高的频率下采样的单个场的观测。我们还考虑了未知的相关结构的情况下的学生化统计。结果的动机是宇宙学数据或高频金融数据集的分析，特别是对高斯性和各向同性测试的兴趣
英文摘要：
We prove a 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 cosmological data or high-frequency financial data sets, with a particular interest towards testing for Gaussianity and isotropy
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
