A consistent test of equality of distributions for Hilbert-valued random elements

IF 1.4 3区 数学 Q2 STATISTICS & PROBABILITY
Gil González–Rodríguez , Ana Colubi , Wenceslao González–Manteiga , Manuel Febrero–Bande
{"title":"A consistent test of equality of distributions for Hilbert-valued random elements","authors":"Gil González–Rodríguez ,&nbsp;Ana Colubi ,&nbsp;Wenceslao González–Manteiga ,&nbsp;Manuel Febrero–Bande","doi":"10.1016/j.jmva.2024.105312","DOIUrl":null,"url":null,"abstract":"<div><p>Two independent random elements taking values in a separable Hilbert space are considered. The aim is to develop a test with bootstrap calibration to check whether they have the same distribution or not. A transformation of both random elements into a new separable Hilbert space is considered so that the equality of expectations of the transformed random elements is equivalent to the equality of distributions. Thus, a bootstrap test procedure to check the equality of means can be used in order to solve the original problem. It will be shown that both the asymptotic and bootstrap approaches proposed are asymptotically correct and consistent. The results can be applied, for example, in functional data analysis. In practice, the test can be solved with simple operations in the original space without applying the mentioned transformation, which is used only to guarantee the theoretical results. Empirical results and comparisons with related methods support and complement the theory.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000198/pdfft?md5=6bc123f9555c6b95bcd432fc26329ddb&pid=1-s2.0-S0047259X24000198-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Multivariate Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0047259X24000198","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0

Abstract

Two independent random elements taking values in a separable Hilbert space are considered. The aim is to develop a test with bootstrap calibration to check whether they have the same distribution or not. A transformation of both random elements into a new separable Hilbert space is considered so that the equality of expectations of the transformed random elements is equivalent to the equality of distributions. Thus, a bootstrap test procedure to check the equality of means can be used in order to solve the original problem. It will be shown that both the asymptotic and bootstrap approaches proposed are asymptotically correct and consistent. The results can be applied, for example, in functional data analysis. In practice, the test can be solved with simple operations in the original space without applying the mentioned transformation, which is used only to guarantee the theoretical results. Empirical results and comparisons with related methods support and complement the theory.

希尔伯特值随机元素分布相等的一致性检验
研究考虑了在可分离的希尔伯特空间取值的两个独立随机元素。目的是开发一种自举校准检验方法,以检查它们是否具有相同的分布。考虑将两个随机元素变换到一个新的可分离的希尔伯特空间,这样变换后的随机元素的期望相等就等同于分布相等。因此,可以使用自举检验程序来检查均值是否相等,从而解决原始问题。我们将证明所提出的渐进方法和引导方法在渐进上都是正确和一致的。这些结果可用于函数数据分析等。在实践中,只需在原始空间中进行简单的操作就能解决测试问题,而无需应用上述转换,因为转换只是为了保证理论结果。经验结果以及与相关方法的比较支持并补充了理论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Journal of Multivariate Analysis
Journal of Multivariate Analysis 数学-统计学与概率论
CiteScore
2.40
自引率
25.00%
发文量
108
审稿时长
74 days
期刊介绍: Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data. The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of Copula modeling Functional data analysis Graphical modeling High-dimensional data analysis Image analysis Multivariate extreme-value theory Sparse modeling Spatial statistics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信