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| Abstract |
When independent random variables $ X_i $ $ ( i = 1, 2, cdots, k ) $ have probability density $ f_{\theta_i} $, with monotone likelihood ratio respectively, we consider testing $ H_0 : mathrm{min} (\t...heta_1, \theta_2, cdots, \theta_k) = \theta^ast $ vs. $ H_1 : mathrm{min} (\theta_1, \theta_2, cdots, \theta_k) > \theta^ast $ for a constant $ \theta^ast $. We give a class of similar tests and find an unbiased test in this class. We apply and extend the arrangement ordering arguments. It is also proved that this unbiased test has a monotone power function. A modification to testing $ H_0^ast : mathrm{min} (\theta_1, \theta_2, cdots, \theta_k) leqq \theta^ast $ vs. $ H_1 $ is also considered.show more
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