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Robust sequential testing. (English) Zbl 0588.62136
The author considers the asymptotic minimax property of the sequential probability ratio test (SPRT) when the given distributions $$P_{+\epsilon}$$ and $$P_{-\epsilon}$$ contain a small amount of contamination. Let $$N_{+\epsilon}$$ and $$N_{-\epsilon}$$ be the neighborhoods of $$P_{+\epsilon}$$ and $$P_{-\epsilon}$$, respectively. Suppose that $$P_{\epsilon}$$ and $$P_{-\epsilon}$$ approach each other as $$\epsilon$$ tends to zero and that $$N_{+\epsilon}$$ and $$N_{- \epsilon}$$ shrink at an appropriate rate.
Under suitable regularity conditions it is proved that the SPRT based on the least favorable pair of distributions $$(Q_{+\epsilon},Q_{- \epsilon})$$ as defined by P. J. Huber [Ann. Math. Stat. 36, 1753- 1758 (1965; Zbl 0137.127)] is asymptotically least favorable for expected sample size and is asymptotically minimax, provided that the limiting maximum error probabilities are no greater than 1/2.
Reviewer: V.Mammitzsch

##### MSC:
 62L10 Sequential statistical analysis 62F35 Robustness and adaptive procedures (parametric inference)
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