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Abstract:
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In this study, we propose an estimation method for normal mean problem that can have both unknown sparsity in the signals as well as correlation among the signals. Our proposed method first decomposes arbitrary dependent covariance matrix of the observed signals into two parts: common dependence and weakly dependent error terms. By subtracting common dependence, the correlations among the signals are significantly weakened. Then the sparsity is estimated using an empirical Bayesian method based on the likelihood of the signals with the common dependence removed. Using simulated examples that have different degrees of sparsity and a number of dependent structures in the signals, we demonstrate that the performance of our proposed algorithm is favorable compared to the existing method which assumes that signals are independent identically distributed. Furthermore, our approach is applied on real data set which is widely used in other genome-wide association studies (GWAS) research, and it can successfully identify the single-nucleotide polymorphisms (SNPs) on fat mass and obesity-associated (FTO) gene associated with body mass index (BMI), which is consistent with previous findings.
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