{"title":"Is the effective sample size always less than n? A spatial regression approach","authors":"Clemente Ferrer, Ronny Vallejos","doi":"10.1016/j.spl.2024.110309","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, within a spatial statistics framework, we present an upper bound for the effective sample size (ESS) as defined by Vallejos and Osorio (2014), addressing a research gap regarding the mathematical properties of the ESS. There are certain correlation structures for which the ESS exceeds <span><math><mi>n</mi></math></span>, which is inconsistent with the maximum possible sample size. Our approach identifies conditions on the correlation matrix of a spatial process that ensure that the equivalent number of independent and identically distributed observations within a spatial sample of size <span><math><mi>n</mi></math></span> does not exceed <span><math><mi>n</mi></math></span>. This property is desirable because it ensures the effectiveness of reduction measures.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110309"},"PeriodicalIF":0.9000,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics & Probability Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167715224002785","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: 0
Abstract
In this paper, within a spatial statistics framework, we present an upper bound for the effective sample size (ESS) as defined by Vallejos and Osorio (2014), addressing a research gap regarding the mathematical properties of the ESS. There are certain correlation structures for which the ESS exceeds , which is inconsistent with the maximum possible sample size. Our approach identifies conditions on the correlation matrix of a spatial process that ensure that the equivalent number of independent and identically distributed observations within a spatial sample of size does not exceed . This property is desirable because it ensures the effectiveness of reduction measures.
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Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature.
Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission.
The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability.
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