{"title":"多元正态均值向量的多交叉序贯固定大小置信区域方法","authors":"Nitis Mukhopadhyay, Sankha Muthu Poruthotage","doi":"10.1016/j.stamet.2014.03.003","DOIUrl":null,"url":null,"abstract":"<div><p>The <em>asymptotically efficient</em> and <em>asymptotically consistent</em><span> purely sequential procedure of Mukhopadhyay and Al-Mousawi (1986) is customarily used to construct a confidence region </span><span><math><mi>R</mi></math></span> for the mean vector <span><math><mstyle><mi>μ</mi></mstyle></math></span> of <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub><mrow><mo>(</mo><mstyle><mi>μ</mi></mstyle><mo>,</mo><msup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msup><mstyle><mi>H</mi></mstyle><mo>)</mo></mrow></math></span>. This procedure does not have the <em>exact consistency</em> property. <span><math><msub><mrow><mstyle><mi>H</mi></mstyle></mrow><mrow><mi>p</mi><mo>×</mo><mi>p</mi></mrow></msub></math></span> is assumed known and positive definite with <span><math><msup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> unknown. The maximum diameter of <span><math><mi>R</mi></math></span><span> and the confidence coefficient are prefixed.</span></p><p><span>A purely sequential sampling strategy is proposed allowing sampling until sample size crosses the boundary multiple times. We ascertain asymptotic efficiency and asymptotic consistency properties (</span><span>Theorem 3.1</span><span>). Its ability to nearly achieve required coverage probability without significant over-sampling is demonstrated with simulations. A truncation technique plus fine-tuning of the multiple crossing rule are proposed to increase practicality. Two real data illustrations are highlighted.</span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2014-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2014.03.003","citationCount":"2","resultStr":"{\"title\":\"Multiple crossing sequential fixed-size confidence region methodologies for a multivariate normal mean vector\",\"authors\":\"Nitis Mukhopadhyay, Sankha Muthu Poruthotage\",\"doi\":\"10.1016/j.stamet.2014.03.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The <em>asymptotically efficient</em> and <em>asymptotically consistent</em><span> purely sequential procedure of Mukhopadhyay and Al-Mousawi (1986) is customarily used to construct a confidence region </span><span><math><mi>R</mi></math></span> for the mean vector <span><math><mstyle><mi>μ</mi></mstyle></math></span> of <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub><mrow><mo>(</mo><mstyle><mi>μ</mi></mstyle><mo>,</mo><msup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msup><mstyle><mi>H</mi></mstyle><mo>)</mo></mrow></math></span>. This procedure does not have the <em>exact consistency</em> property. <span><math><msub><mrow><mstyle><mi>H</mi></mstyle></mrow><mrow><mi>p</mi><mo>×</mo><mi>p</mi></mrow></msub></math></span> is assumed known and positive definite with <span><math><msup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> unknown. The maximum diameter of <span><math><mi>R</mi></math></span><span> and the confidence coefficient are prefixed.</span></p><p><span>A purely sequential sampling strategy is proposed allowing sampling until sample size crosses the boundary multiple times. We ascertain asymptotic efficiency and asymptotic consistency properties (</span><span>Theorem 3.1</span><span>). Its ability to nearly achieve required coverage probability without significant over-sampling is demonstrated with simulations. A truncation technique plus fine-tuning of the multiple crossing rule are proposed to increase practicality. Two real data illustrations are highlighted.</span></p></div>\",\"PeriodicalId\":48877,\"journal\":{\"name\":\"Statistical Methodology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.stamet.2014.03.003\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistical Methodology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S157231271400029X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methodology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S157231271400029X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q","JCRName":"Mathematics","Score":null,"Total":0}
Multiple crossing sequential fixed-size confidence region methodologies for a multivariate normal mean vector
The asymptotically efficient and asymptotically consistent purely sequential procedure of Mukhopadhyay and Al-Mousawi (1986) is customarily used to construct a confidence region for the mean vector of . This procedure does not have the exact consistency property. is assumed known and positive definite with unknown. The maximum diameter of and the confidence coefficient are prefixed.
A purely sequential sampling strategy is proposed allowing sampling until sample size crosses the boundary multiple times. We ascertain asymptotic efficiency and asymptotic consistency properties (Theorem 3.1). Its ability to nearly achieve required coverage probability without significant over-sampling is demonstrated with simulations. A truncation technique plus fine-tuning of the multiple crossing rule are proposed to increase practicality. Two real data illustrations are highlighted.
期刊介绍:
Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.