Optimal Multistage Sampling in a Boundary-Crossing Problem

Details Optimal Multistage Sampling in a Boundary-Crossing Problem Optimal Multistage Sampling in a Boundary-Crossing Problem

2011-05-11

arxiv.org/abs/1105.2322v1

Mathematics

Statistics Theory

Scientific paper

Brownian motion with known positive drift is sampled in stages until it crosses a positive boundary $a$. A family of multistage samplers that control the expected overshoot over the boundary by varying the stage size at each stage is shown to be optimal for large $a$, minimizing a linear combination of overshoot and number of stages. Applications to hypothesis testing are discussed.

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