文章基本信息

标题：On model selection consistency of regularized M-estimators
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作者：Jason D. Lee ; Yuekai Sun ; Jonathan E. Taylor 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2015
卷号：9
期号：1
页码：608-642
DOI：10.1214/15-EJS1013
语种：English
出版社：Institute of Mathematical Statistics
摘要：Regularized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Usually the low-dimensional structure is encoded by the presence of the (unknown) parameters in some low-dimensional model subspace. In such settings, it is desirable for estimates of the model parameters to be model selection consistent: the estimates also fall in the model subspace. We develop a general framework for establishing consistency and model selection consistency of regularized M-estimators and show how it applies to some special cases of interest in statistical learning. Our analysis identifies two key properties of regularized M-estimators, referred to as geometric decomposability and irrepresentability, that ensure the estimators are consistent and model selection consistent.