Almost minimax sequential tests of composite hypotheses

Details Almost minimax sequential tests of composite hypotheses Almost minimax sequential tests of composite hypotheses

2012-04-24

arxiv.org/abs/1204.5291v1

Mathematics

Statistics Theory

33 pages

Scientific paper

The problem of sequentially testing a simple null hypothesis versus a discrete, composite alternative hypothesis is considered. We study sequential tests that use weighted generalized likelihood ratio statistics and mixture-based likelihood ratio statistics. It is shown that both tests have two kinds of asymptotic optimality as error probabilities go to zero. First, for any weights, they minimize asymptotically to first order the expected sample size under every possible state of the world. Second, with an appropriate selection of weights, they minimize asymptotically within a negligible term the expected Kullback--Leibler information in the least favorable situation. Finally, we compare the performance of the two tests using simulation experiments, which agree with the results of our asymptotic analysis. Based on Monte Carlo simulations we conclude that the optimized generalized likelihood ratio and mixture-based likelihood ratio tests with specially designed weights perform almost identically.

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