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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Abstract

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

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

Dates
First available in Project Euclid: 17 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032298296

Digital Object Identifier
doi:10.1214/aos/1032298296

Mathematical Reviews number (MathSciNet)
MR1416661

Zentralblatt MATH identifier
0868.62063

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1032298296


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References

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