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Summary. In high dimensional model selection problems, penalized least square approaches have been extensively used. The paper addresses the question of both robustness and efficiency of penalized model selection methods and proposes a data‐driven weighted linear combination of convex loss functions, together with weighted L1‐penalty. It is completely data adaptive and does not require prior knowledge...
Penalized likelihood methods are fundamental to ultrahigh dimensional variable selection. How high dimensionality such methods can handle remains largely unknown. In this paper, we show that in the context of generalized linear models, such methods possess model selection consistency with oracle properties even for dimensionality of nonpolynomial (NP) order of sample size, for a class of penalized...
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