Abstract
We consider the problem of testing the sign of the drift θ of a Brownian motion. As in the preceding section we let the costs depend on the underlying parameter and choose it as “cθ2”, c>0. We show that a certain simple Bayes rule, which defines a repeated significance test, is optimal for the testing problem in a Bayes sense. The simple Bayes rules stop sampling when the posterior mass of the hypothesis or the alternative is too small.
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© 1986 Springer-Verlag Berlin Heidelberg
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Lerche, H.R. (1986). An optimal property of the repeated significance test. In: Boundary Crossing of Brownian Motion. Lecture Notes in Statistics, vol 40. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-6569-7_11
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DOI: https://doi.org/10.1007/978-1-4615-6569-7_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96433-1
Online ISBN: 978-1-4615-6569-7
eBook Packages: Springer Book Archive