Abstract:
The statistical problem of the distinguishing between two hypotheses $H_0$ (the theoretical density of probability is $f(x;0)$) and $H_\theta$ (the theoretical density of probability is $f(x,\theta)$) is considered. It is assumed that an unknown $p$-dimensional parameter may be equal to one of two alternative values 0 and $\theta$ or to some “intermediate” value $\theta_\lambda$.
One approximate variant of the optimum generalized probability ratio test is suggested in this paper. It is shown that the optimum properties of this test are highly near to “ideal” and that the test is better than Wald sequential test.
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