ROBUSTNESS OF THE N-CUSUM STOPPING RULE IN A WIENER DISORDER PROBLEM
We study a Wiener disorder problem of detecting the minimum of N change-points in N observation channels coupled by correlated noises. It is assumed that the observations in each dimension can have different strengths and that the change-points may differ from channel to channel. The objective is th...
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Veröffentlicht in: | The Annals of applied probability 2015-12, Vol.25 (6), p.3405-3433 |
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creator | Zhang, Hongzhong Rodosthenous, Neofytos Hadjiliadis, Olympia |
description | We study a Wiener disorder problem of detecting the minimum of N change-points in N observation channels coupled by correlated noises. It is assumed that the observations in each dimension can have different strengths and that the change-points may differ from channel to channel. The objective is the quickest detection of the minimum of the N change-points. We adopt a min–max approach and consider an extended Lorden's criterion, which is minimized subject to a constraint on the mean time to the first false alarm. It is seen that, under partial information of the post-change drifts and a general nonsingular stochastic correlation structure in the noises, the minimum of N cumulative sums (CUSUM) stopping rules is asymptotically optimal as the mean time to the first false alarm increases without bound. We further discuss applications of this result with emphasis on its implications to the efficiency of the decentralized versus the centralized systems of observations which arise in engineering. |
doi_str_mv | 10.1214/14-AAP1078 |
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It is assumed that the observations in each dimension can have different strengths and that the change-points may differ from channel to channel. The objective is the quickest detection of the minimum of the N change-points. We adopt a min–max approach and consider an extended Lorden's criterion, which is minimized subject to a constraint on the mean time to the first false alarm. It is seen that, under partial information of the post-change drifts and a general nonsingular stochastic correlation structure in the noises, the minimum of N cumulative sums (CUSUM) stopping rules is asymptotically optimal as the mean time to the first false alarm increases without bound. We further discuss applications of this result with emphasis on its implications to the efficiency of the decentralized versus the centralized systems of observations which arise in engineering.</description><identifier>ISSN: 1050-5164</identifier><identifier>EISSN: 2168-8737</identifier><identifier>DOI: 10.1214/14-AAP1078</identifier><language>eng</language><publisher>Hayward: Institute of Mathematical Statistics</publisher><subject>60G40 ; 60K35 ; 62C20 ; 62L10 ; 62L15 ; Asymptotic methods ; correlated noise ; Correlation analysis ; CUSUM ; Noise ; quickest detection ; Stochastic models ; Wiener disorder problem</subject><ispartof>The Annals of applied probability, 2015-12, Vol.25 (6), p.3405-3433</ispartof><rights>Copyright © 2015 Institute of Mathematical Statistics</rights><rights>Copyright Institute of Mathematical Statistics Dec 2015</rights><rights>Copyright 2015 Institute of Mathematical Statistics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c416t-621a0527971a34e25e2b985f29631251179678400e7c458bc418b34f05ad99943</citedby><cites>FETCH-LOGICAL-c416t-621a0527971a34e25e2b985f29631251179678400e7c458bc418b34f05ad99943</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/24521660$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/24521660$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,776,780,799,828,881,921,27901,27902,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>Zhang, Hongzhong</creatorcontrib><creatorcontrib>Rodosthenous, Neofytos</creatorcontrib><creatorcontrib>Hadjiliadis, Olympia</creatorcontrib><title>ROBUSTNESS OF THE N-CUSUM STOPPING RULE IN A WIENER DISORDER PROBLEM</title><title>The Annals of applied probability</title><description>We study a Wiener disorder problem of detecting the minimum of N change-points in N observation channels coupled by correlated noises. It is assumed that the observations in each dimension can have different strengths and that the change-points may differ from channel to channel. The objective is the quickest detection of the minimum of the N change-points. We adopt a min–max approach and consider an extended Lorden's criterion, which is minimized subject to a constraint on the mean time to the first false alarm. It is seen that, under partial information of the post-change drifts and a general nonsingular stochastic correlation structure in the noises, the minimum of N cumulative sums (CUSUM) stopping rules is asymptotically optimal as the mean time to the first false alarm increases without bound. We further discuss applications of this result with emphasis on its implications to the efficiency of the decentralized versus the centralized systems of observations which arise in engineering.</description><subject>60G40</subject><subject>60K35</subject><subject>62C20</subject><subject>62L10</subject><subject>62L15</subject><subject>Asymptotic methods</subject><subject>correlated noise</subject><subject>Correlation analysis</subject><subject>CUSUM</subject><subject>Noise</subject><subject>quickest detection</subject><subject>Stochastic models</subject><subject>Wiener disorder problem</subject><issn>1050-5164</issn><issn>2168-8737</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNo9kE1rg0AQhpfSQtO0l94LC70VbHf2w909WmMSwaj4QY9ijEIkramaQ_99N0RymmF45pnhRegZyDtQ4B_ALceJgUh1g2YUbGUpyeQtmgERxBJg83v0MAwtIURzLWdokUSfeZqFXpriaImztYdDy83TfIPTLIpjP1zhJA887IfYwV--F3oJXvhplCxME5vtwNs8orumPAz101TnKF96mbu2gmjlu05gVRzs0bIplERQqSWUjNdU1HSrlWiothlQASC1LRUnpJYVF2prttSW8YaIcqe15myOnIv32HdtXY31qTrsd8Wx33-X_V_RlfvCzYNpOpWyK48FcM4kYVIq43i9On5P9TAWbXfqf8zbBUiTmE2FDYZ6u1BV3w1DXzfXI0CKc9JGWUxJG_jlArfD2PVXknJx9hH2D8XFcSE</recordid><startdate>20151201</startdate><enddate>20151201</enddate><creator>Zhang, Hongzhong</creator><creator>Rodosthenous, Neofytos</creator><creator>Hadjiliadis, Olympia</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20151201</creationdate><title>ROBUSTNESS OF THE N-CUSUM STOPPING RULE IN A WIENER DISORDER PROBLEM</title><author>Zhang, Hongzhong ; Rodosthenous, Neofytos ; Hadjiliadis, Olympia</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c416t-621a0527971a34e25e2b985f29631251179678400e7c458bc418b34f05ad99943</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>60G40</topic><topic>60K35</topic><topic>62C20</topic><topic>62L10</topic><topic>62L15</topic><topic>Asymptotic methods</topic><topic>correlated noise</topic><topic>Correlation analysis</topic><topic>CUSUM</topic><topic>Noise</topic><topic>quickest detection</topic><topic>Stochastic models</topic><topic>Wiener disorder problem</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Hongzhong</creatorcontrib><creatorcontrib>Rodosthenous, Neofytos</creatorcontrib><creatorcontrib>Hadjiliadis, Olympia</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>The Annals of applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Hongzhong</au><au>Rodosthenous, Neofytos</au><au>Hadjiliadis, Olympia</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ROBUSTNESS OF THE N-CUSUM STOPPING RULE IN A WIENER DISORDER PROBLEM</atitle><jtitle>The Annals of applied probability</jtitle><date>2015-12-01</date><risdate>2015</risdate><volume>25</volume><issue>6</issue><spage>3405</spage><epage>3433</epage><pages>3405-3433</pages><issn>1050-5164</issn><eissn>2168-8737</eissn><abstract>We study a Wiener disorder problem of detecting the minimum of N change-points in N observation channels coupled by correlated noises. It is assumed that the observations in each dimension can have different strengths and that the change-points may differ from channel to channel. The objective is the quickest detection of the minimum of the N change-points. We adopt a min–max approach and consider an extended Lorden's criterion, which is minimized subject to a constraint on the mean time to the first false alarm. It is seen that, under partial information of the post-change drifts and a general nonsingular stochastic correlation structure in the noises, the minimum of N cumulative sums (CUSUM) stopping rules is asymptotically optimal as the mean time to the first false alarm increases without bound. We further discuss applications of this result with emphasis on its implications to the efficiency of the decentralized versus the centralized systems of observations which arise in engineering.</abstract><cop>Hayward</cop><pub>Institute of Mathematical Statistics</pub><doi>10.1214/14-AAP1078</doi><tpages>29</tpages><oa>free_for_read</oa></addata></record> |
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subjects | 60G40 60K35 62C20 62L10 62L15 Asymptotic methods correlated noise Correlation analysis CUSUM Noise quickest detection Stochastic models Wiener disorder problem |
title | ROBUSTNESS OF THE N-CUSUM STOPPING RULE IN A WIENER DISORDER PROBLEM |
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