Robust hypothesis testing for asymmetric nominal densities under a relative entropy tolerance |
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Authors: | Enbin Song Qingjiang Shi Yunmin Zhu Jianxi Pan |
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Institution: | 1.Department of Mathematics and Center for Statistical Science,Sichuan University,Chengdu,China;2.School of Information Science and Technology,Zhejiang Sci-Tech University,Hangzhou,China |
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Abstract: | In this paper, we address an open problem raised by Levy (2009) regarding the design of a binary minimax test without the symmetry assumption on the nominal conditional probability densities of observations. In the binary minimax test, the nominal likelihood ratio is a monotonically increasing function and the probability densities of the observations are located in neighborhoods characterized by placing a bound on the relative entropy between the actual and nominal densities. The general minimax testing problem at hand is an infinite-dimensional optimization problem, which is quite difficult to solve. In this paper, we prove that the complicated minimax testing problem can be substantially reduced to solve a nonlinear system of two equations having only two unknown variables, which provides an efficient numerical solution. |
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