The Annals of Statistics

Boundary Crossing Probabilities and Statistical Applications

David Siegmund

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Abstract

This paper surveys recent results involving boundary crossing probabilities and related statistical applications. The first part is concerned with problems of sequential analysis, especially repeated significance tests and their application to sequential clinical trials involving survival data. The second part develops the probability theory motivated by the problems of Part 1. A method for computing first passage distributions of Brownian motion to linear boundaries is introduced and then modified to handle problems problems in discrete time and those involving nonlinear boundaries. The third part is concerned with fixed sample statistical problems, especially change-point problems, which involve boundary crossing probabilities. Examples are given of problems for which the methods of Part 2 appear adequate and of problems which require new methods.

Article information

Source
Ann. Statist., Volume 14, Number 2 (1986), 361-404.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349928

Digital Object Identifier
doi:10.1214/aos/1176349928

Mathematical Reviews number (MathSciNet)
MR840504

Zentralblatt MATH identifier
0632.62077

JSTOR
links.jstor.org

Subjects
Primary: 62L10: Sequential analysis

Keywords
Sequential test change point Brownian motion large deviations

Citation

Siegmund, David. Boundary Crossing Probabilities and Statistical Applications. Ann. Statist. 14 (1986), no. 2, 361--404. doi:10.1214/aos/1176349928. https://projecteuclid.org/euclid.aos/1176349928


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