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This paper is motivated by a regression analysis of electroencephalography (EEG) neuroimaging data with high-dimensional correlated responses with multi-level nested correlations. We develop a divide-and-conquer procedure implemented in a fully distributed and parallelized computational scheme for statistical estimation and inference of regression parameters. Despite significant efforts in the literature, the computational bottleneck associated with high-dimensional likelihoods prevents the scalability of existing methods. The proposed m
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