{"title":"测试同质性:稀疏函数数据的麻烦。","authors":"Changbo Zhu, Jane-Ling Wang","doi":"10.1093/jrsssb/qkad021","DOIUrl":null,"url":null,"abstract":"<p><p>Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be done for such data. In particular, we show that testing the marginal homogeneity based on point-wise distributions is feasible under some mild constraints and propose a new two-sample statistic that works well with both intensively and sparsely measured functional data. The proposed test statistic is formulated upon energy distance, and the convergence rate of the test statistic to its population version is derived along with the consistency of the associated permutation test. The aptness of our method is demonstrated on both synthetic and real data sets.</p>","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"85 3","pages":"705-731"},"PeriodicalIF":3.1000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ftp.ncbi.nlm.nih.gov/pub/pmc/oa_pdf/48/e2/qkad021.PMC10376451.pdf","citationCount":"0","resultStr":"{\"title\":\"Testing homogeneity: the trouble with sparse functional data.\",\"authors\":\"Changbo Zhu, Jane-Ling Wang\",\"doi\":\"10.1093/jrsssb/qkad021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be done for such data. In particular, we show that testing the marginal homogeneity based on point-wise distributions is feasible under some mild constraints and propose a new two-sample statistic that works well with both intensively and sparsely measured functional data. The proposed test statistic is formulated upon energy distance, and the convergence rate of the test statistic to its population version is derived along with the consistency of the associated permutation test. The aptness of our method is demonstrated on both synthetic and real data sets.</p>\",\"PeriodicalId\":49982,\"journal\":{\"name\":\"Journal of the Royal Statistical Society Series B-Statistical Methodology\",\"volume\":\"85 3\",\"pages\":\"705-731\"},\"PeriodicalIF\":3.1000,\"publicationDate\":\"2023-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://ftp.ncbi.nlm.nih.gov/pub/pmc/oa_pdf/48/e2/qkad021.PMC10376451.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Royal Statistical Society Series B-Statistical Methodology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1093/jrsssb/qkad021\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Royal Statistical Society Series B-Statistical Methodology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/jrsssb/qkad021","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Testing homogeneity: the trouble with sparse functional data.
Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be done for such data. In particular, we show that testing the marginal homogeneity based on point-wise distributions is feasible under some mild constraints and propose a new two-sample statistic that works well with both intensively and sparsely measured functional data. The proposed test statistic is formulated upon energy distance, and the convergence rate of the test statistic to its population version is derived along with the consistency of the associated permutation test. The aptness of our method is demonstrated on both synthetic and real data sets.
期刊介绍：
Series B (Statistical Methodology) aims to publish high quality papers on the methodological aspects of statistics and data science more broadly. The objective of papers should be to contribute to the understanding of statistical methodology and/or to develop and improve statistical methods; any mathematical theory should be directed towards these aims. The kinds of contribution considered include descriptions of new methods of collecting or analysing data, with the underlying theory, an indication of the scope of application and preferably a real example. Also considered are comparisons, critical evaluations and new applications of existing methods, contributions to probability theory which have a clear practical bearing (including the formulation and analysis of stochastic models), statistical computation or simulation where original methodology is involved and original contributions to the foundations of statistical science. Reviews of methodological techniques are also considered. A paper, even if correct and well presented, is likely to be rejected if it only presents straightforward special cases of previously published work, if it is of mathematical interest only, if it is too long in relation to the importance of the new material that it contains or if it is dominated by computations or simulations of a routine nature.
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