## 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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