The Annals of Statistics

A note on Ritov's Bayes approach to the minimax property of the cusum procedure

M. Beibel

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We consider, in a Bayesian framework, the model $W_t = B_t + \theta (t - \nu)^+$, where B is a standard Brownian motion, $\theta$ is arbitrary but known and $\nu$ is the unknown change-point. We transfer the construction of Ritov to this continuous time setup and show that the corresponding Bayes problems can be reduced to generalized parking problems.

Article information

Ann. Statist., Volume 24, Number 4 (1996), 1804-1812.

First available in Project Euclid: 17 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62L10: Sequential analysis
Secondary: 62L15: Optimal stopping [See also 60G40, 91A60] 62C10: Bayesian problems; characterization of Bayes procedures

Change-point cusum procedures sequential detection Wiener process generalized parking problems


Beibel, M. A note on Ritov's Bayes approach to the minimax property of the cusum procedure. Ann. Statist. 24 (1996), no. 4, 1804--1812. doi:10.1214/aos/1032298296.

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