Bayesian inference for the proportion of true null hypotheses using minimum Hellinger distance |
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Authors: | Moonsu Kang Jaewon Lee |
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Affiliation: | a Institute for Statistics, Department of Statistics, Korea University, Seoul 136-701, Republic of Korea b Department of Statistics, Korea University, Seoul 136-701, Republic of Korea |
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Abstract: | It is important that the proportion of true null hypotheses be estimated accurately in a multiple hypothesis context. Current estimation methods, however, are not suitable for high-dimensional data such as microarray data. First, they do not consider the (strong) dependence between hypotheses (or genes), thereby resulting in inaccurate estimation. Second, the unknown distribution of false null hypotheses cannot be estimated properly by these methods. Third, the estimation is affected strongly by outliers. In this paper, we find out the optimal procedure for estimating the proportion of true null hypotheses under a (strong) dependence based on the Dirichlet process prior. In addition, by using the minimum Hellinger distance, the estimation should be robust to any model misspecification as well as to any outliers while maintaining efficiency. The results are confirmed by a simulation study, and the newly developed methodology is illustrated by a real microarray data. |
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Keywords: | Proportion of true null Strong dependence Dirichlet process Minimum Hellinger distance IWMDE Microarray |
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