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# Open-Ended Tests for Koopman-Darmois Families

Gary Lorden
The Annals of Statistics
Vol. 1, No. 4 (Jul., 1973), pp. 633-643
Stable URL: http://www.jstor.org/stable/2958308
Page Count: 11
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## Abstract

The generalized likelihood ratio is used to define a stopping rule for rejecting the null hypothesis θ = θ0 in favor of $\theta > \theta_0$. Subject to a bound α on the probability of ever stopping in case θ = θ0, the expected sample sizes for $\theta > \theta_0$ are minimized within a multiple of log log α-1, the multiple depending on θ. An heuristic bound on the error probability of a likelihood ratio procedure is derived and verified in the case of a normal mean by consideration of a Wiener process. Useful lower bounds on the small-sample efficiency in the normal case are thereby obtained.

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