Testing for the Maximum Mean in a Mixture of Normals.

摘要

We consider the test of the null hypothesis that the largest mean in a mixture of an unknown number of normal components is less than or equal to a given threshold. This test is motivated by the problem of assessing whether the Soviet Union has been operating in compliance with the Nuclear Test Ban Treaty. In our analysis, the number of normal components is determined using Akaike's Information Criterion while the hypothesis test itself is based on asymptotic results given by Behboodian for a mixture of two normal computers. A bootstrap approach is also considered for estimating the standard error of the largest estimated mean. The performance of the tests are examined through the use of simulation. Keywords: Reprints. (kr)