Abstract
A Wiener process with unknown drift parameter μ is, beginning at O, observed continuously and one has to decide between the hypotheses μ≤0 and μ>0. For loss functions of the form sμr and linear cost functions one wants to determine a minimax sequential test. Generalizing the results of DeGroot (1960) a minimax test in the class of all symmetrical SPRT’s is given in an explicit form. On the other hand it is shown that this SPRT is, in general, no longer minimax in the class of all sequential tests.
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References
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Schmitz, N. Minimax sequential tests of composite hypotheses on the drift of a Wiener process. Statistische Hefte 28, 247–261 (1987). https://doi.org/10.1007/BF02932605
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DOI: https://doi.org/10.1007/BF02932605