{"title":"一种综合的局部深度测量","authors":"Lucas Fernandez-Piana, Marcela Svarc","doi":"10.1007/s10182-021-00424-6","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce the Integrated Dual Local Depth, which is a local depth measure for data in a Banach space based on the use of one-dimensional projections. The properties of a depth measure are analyzed under this setting and a proper definition of local symmetry is given. Moreover, strong consistency results for the local depth and also, for local depth regions are attained. Finally, applications to descriptive data analysis and classification are analyzed, making a special focus on multivariate functional data, where we obtain very promising results.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":"106 2","pages":"175 - 197"},"PeriodicalIF":1.4000,"publicationDate":"2022-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10182-021-00424-6.pdf","citationCount":"0","resultStr":"{\"title\":\"An integrated local depth measure\",\"authors\":\"Lucas Fernandez-Piana, Marcela Svarc\",\"doi\":\"10.1007/s10182-021-00424-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We introduce the Integrated Dual Local Depth, which is a local depth measure for data in a Banach space based on the use of one-dimensional projections. The properties of a depth measure are analyzed under this setting and a proper definition of local symmetry is given. Moreover, strong consistency results for the local depth and also, for local depth regions are attained. Finally, applications to descriptive data analysis and classification are analyzed, making a special focus on multivariate functional data, where we obtain very promising results.</p></div>\",\"PeriodicalId\":55446,\"journal\":{\"name\":\"Asta-Advances in Statistical Analysis\",\"volume\":\"106 2\",\"pages\":\"175 - 197\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2022-01-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10182-021-00424-6.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asta-Advances in Statistical Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10182-021-00424-6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asta-Advances in Statistical Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10182-021-00424-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
We introduce the Integrated Dual Local Depth, which is a local depth measure for data in a Banach space based on the use of one-dimensional projections. The properties of a depth measure are analyzed under this setting and a proper definition of local symmetry is given. Moreover, strong consistency results for the local depth and also, for local depth regions are attained. Finally, applications to descriptive data analysis and classification are analyzed, making a special focus on multivariate functional data, where we obtain very promising results.
期刊介绍：
AStA - Advances in Statistical Analysis, a journal of the German Statistical Society, is published quarterly and presents original contributions on statistical methods and applications and review articles.
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