{"title":"Kernel Mean Embedding of Probability Measures and its Applications to Functional Data Analysis","authors":"Saeed Hayati, Kenji Fukumizu, Afshin Parvardeh","doi":"10.1111/sjos.12691","DOIUrl":null,"url":null,"abstract":"Abstract This study intends to introduce kernel mean embedding of probability measures over infinite‐dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of probability measures in small open neighborhoods, which identifies a pseudo‐likelihood and fosters a rich framework for statistical inference. Utilizing Maximum Mean Discrepancy, we devise new tests in functional response models. The performance of new derived tests is evaluated against competitors in three major problems in functional data analysis including function‐on‐scalar regression, functional one‐way ANOVA, and equality of covariance operators. This article is protected by copyright. All rights reserved.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scandinavian Journal of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1111/sjos.12691","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 3
Abstract
Abstract This study intends to introduce kernel mean embedding of probability measures over infinite‐dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of probability measures in small open neighborhoods, which identifies a pseudo‐likelihood and fosters a rich framework for statistical inference. Utilizing Maximum Mean Discrepancy, we devise new tests in functional response models. The performance of new derived tests is evaluated against competitors in three major problems in functional data analysis including function‐on‐scalar regression, functional one‐way ANOVA, and equality of covariance operators. This article is protected by copyright. All rights reserved.
期刊介绍：
The Scandinavian Journal of Statistics is internationally recognised as one of the leading statistical journals in the world. It was founded in 1974 by four Scandinavian statistical societies. Today more than eighty per cent of the manuscripts are submitted from outside Scandinavia.
It is an international journal devoted to reporting significant and innovative original contributions to statistical methodology, both theory and applications.
The journal specializes in statistical modelling showing particular appreciation of the underlying substantive research problems.
The emergence of specialized methods for analysing longitudinal and spatial data is just one example of an area of important methodological development in which the Scandinavian Journal of Statistics has a particular niche.
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