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Abstract:
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In this study, we propose an estimation method for the normal mean problem that can adapt to the sparsity of the signals as well as take correlation among the signals into consideration. The proposed method effectively decomposes arbitrary dependent covariance matrix of observed signals into two parts: common dependence and weakly dependent error terms. By subtracting common dependence, the correlation among the signals are significantly weakened. Then the sparsity are estimated by empirical Bayesian method based on the likelihood of the signals removing the common dependence. As demonstrated in the simulated examples with several different dependent structures of signals, our estimate of sparsity compares favorably with traditional method which considers the signals are identical independent distributed. Furthermore, our approach is illustrated by genome-wide data set and successfully identify the Single nucleotide polymorphisms (SNPs) on FTO gene associated with body mass index (BMI).
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