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Topics in high-dimensional inference
This thesis concerns three connected problems in high-dimensional inference: compound estimation of normal means, nonparametric regression and penalization method for variable selection.In the first part of the thesis, we propose a general maximum likelihood empirical Bayes (GMLEB) method for the compound estimation of normal means. We prove that under mild moment conditions on the unknown means, the GMLEB enjoys the adaptive ration optimality and adaptive minimaxity. Simulation experimentsdoi:10.7282/t3xk8fq5 fatcat:gcokqbgb6reo5metw5gmiyf5gm