TY - JOUR
T1 - Optimality properties of the shiryaev-roberts procedure
AU - Pollak, Moshe
AU - Tartakovsky, Alexander G.
PY - 2009/10
Y1 - 2009/10
N2 - In 1961, for detecting a change in the drift of a Brownian motion, Shiryaev introduced what is now usually referred to as the Shiryaev-Roberts procedure. This procedure has a number of optimality and asymptotic optimality properties in various settings. Shiryaev (1961, 1963), and more recently Feinberg and Shiryaev (2006), established exact optimality properties in the context of monitoring a Brownian motion for a (known) change of drift. Their method of proof relies on techniques particular to Brownian motion that are not applicable in discrete time. Here we establish analogous results in a general discrete time setting, where surveillance is not relegated to a change of mean or to normal observations only. Our method of proof relies on asymptotic Bayesian analysis and on renewal theory.
AB - In 1961, for detecting a change in the drift of a Brownian motion, Shiryaev introduced what is now usually referred to as the Shiryaev-Roberts procedure. This procedure has a number of optimality and asymptotic optimality properties in various settings. Shiryaev (1961, 1963), and more recently Feinberg and Shiryaev (2006), established exact optimality properties in the context of monitoring a Brownian motion for a (known) change of drift. Their method of proof relies on techniques particular to Brownian motion that are not applicable in discrete time. Here we establish analogous results in a general discrete time setting, where surveillance is not relegated to a change of mean or to normal observations only. Our method of proof relies on asymptotic Bayesian analysis and on renewal theory.
KW - Changepoint problems
KW - Cusum procedures
KW - Sequential detection
KW - Shiryaev-roberts procedures
UR - http://www.scopus.com/inward/record.url?scp=70249085400&partnerID=8YFLogxK
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AN - SCOPUS:70249085400
SN - 1017-0405
VL - 19
SP - 1729
EP - 1739
JO - Statistica Sinica
JF - Statistica Sinica
IS - 4
ER -