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Abstract:
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Motivated by recent genome-wide association studies in admixed/trans-ethnic population, we are interested in estimation and inference of high dimensional mixed effect generalized linear models. These models are widely applicable to many fields, including gene mapping studies of disease outcomes and other phenotypes of interest in the presence of various confounding effects. The high dimensional models we concern often possess non-convex and non-smooth objective functions. We propose a new stochastic perturbed ADMM algorithm to estimate the model. Simulation studies show that our algorithm performs comparably to a new stochastic proximal gradient algorithm proposed by Atchad\'e et al. 2014. We develop the non-convex and stochastic convergence theory for the proximal algorithm, which initializes our route for statistical and computational theory development of the proposed methods.
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