Minimax optimality of the Shiryayev-Roberts change-point detection rule

D. O. Siegmund; B. Yakir

doi:10.1016/j.jspi.2008.03.016

Minimax optimality of the Shiryayev-Roberts change-point detection rule

D. O. Siegmund^*, B. Yakir

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

The result of Pollak [1985. Optimal detection of a change in distribution. Ann. Statist. 13, 206-227] proving the asymptotic optimality in sequential change-point detection of a suitable Shirayayev-Roberts stopping rule up to terms that vanish in the limit is generalized from the case of two completely specified distributions to that of a composite alternative hypothesis in a multidimensional exponential family. An explicit asymptotic lower bound on the expected Kullback-Leibler information required to detect a change-point is derived and is shown to be attained by a Shirayayev-Roberts stopping rule.

Original language	English
Pages (from-to)	2815-2825
Number of pages	11
Journal	Journal of Statistical Planning and Inference
Volume	138
Issue number	9
DOIs	https://doi.org/10.1016/j.jspi.2008.03.016
State	Published - 1 Sep 2008

Bibliographical note

Funding Information:
This work have been supported by the NSF and the US-Israel Binational Science Foundation.

Keywords

Change-point
Minimax optimality
Sequential detection

Access to Document

10.1016/j.jspi.2008.03.016

Cite this

@article{2cbb2afab58c4c0ea8bdfa46b948de88,

title = "Minimax optimality of the Shiryayev-Roberts change-point detection rule",

abstract = "The result of Pollak [1985. Optimal detection of a change in distribution. Ann. Statist. 13, 206-227] proving the asymptotic optimality in sequential change-point detection of a suitable Shirayayev-Roberts stopping rule up to terms that vanish in the limit is generalized from the case of two completely specified distributions to that of a composite alternative hypothesis in a multidimensional exponential family. An explicit asymptotic lower bound on the expected Kullback-Leibler information required to detect a change-point is derived and is shown to be attained by a Shirayayev-Roberts stopping rule.",

keywords = "Change-point, Minimax optimality, Sequential detection",

author = "Siegmund, {D. O.} and B. Yakir",

note = "Funding Information: This work have been supported by the NSF and the US-Israel Binational Science Foundation. ",

year = "2008",

month = sep,

day = "1",

doi = "10.1016/j.jspi.2008.03.016",

language = "אנגלית",

volume = "138",

pages = "2815--2825",

journal = "Journal of Statistical Planning and Inference",

issn = "0378-3758",

publisher = "Elsevier B.V.",

number = "9",

}

TY - JOUR

T1 - Minimax optimality of the Shiryayev-Roberts change-point detection rule

AU - Siegmund, D. O.

AU - Yakir, B.

N1 - Funding Information: This work have been supported by the NSF and the US-Israel Binational Science Foundation.

PY - 2008/9/1

Y1 - 2008/9/1

N2 - The result of Pollak [1985. Optimal detection of a change in distribution. Ann. Statist. 13, 206-227] proving the asymptotic optimality in sequential change-point detection of a suitable Shirayayev-Roberts stopping rule up to terms that vanish in the limit is generalized from the case of two completely specified distributions to that of a composite alternative hypothesis in a multidimensional exponential family. An explicit asymptotic lower bound on the expected Kullback-Leibler information required to detect a change-point is derived and is shown to be attained by a Shirayayev-Roberts stopping rule.

AB - The result of Pollak [1985. Optimal detection of a change in distribution. Ann. Statist. 13, 206-227] proving the asymptotic optimality in sequential change-point detection of a suitable Shirayayev-Roberts stopping rule up to terms that vanish in the limit is generalized from the case of two completely specified distributions to that of a composite alternative hypothesis in a multidimensional exponential family. An explicit asymptotic lower bound on the expected Kullback-Leibler information required to detect a change-point is derived and is shown to be attained by a Shirayayev-Roberts stopping rule.

KW - Change-point

KW - Minimax optimality

KW - Sequential detection

UR - http://www.scopus.com/inward/record.url?scp=43849113475&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2008.03.016

DO - 10.1016/j.jspi.2008.03.016

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:43849113475

SN - 0378-3758

VL - 138

SP - 2815

EP - 2825

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 9

ER -

Minimax optimality of the Shiryayev-Roberts change-point detection rule

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this