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A Bayesian nonparametric sequential test for the mean of a population. (English) Zbl 0585.62137

Summary: We may take observations sequentially from a population with unknown mean \(\theta\). After this sampling stage, we are to decide whether \(\theta\) is greater or less than a known constant \(\nu\). The net worth upon stopping is either \(\theta\) or \(\nu\), respectively, minus sampling costs. The objective is to maximize the expected net worth when the probability measure of the observations is a Dirichlet process with parameter \(\alpha\).
The stopping problem is shown to be truncated when \(\alpha\) has bounded support. The main theorem of the paper leads to bounds on the exact stage of truncation and shows that sampling continues longest on a generalized form of neutral boundary.

MSC:

62L10 Sequential statistical analysis
62L15 Optimal stopping in statistics
62C10 Bayesian problems; characterization of Bayes procedures
62G10 Nonparametric hypothesis testing
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