Abstract
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.
Citation
Jason D. Lee. Yuekai Sun. Jonathan E. Taylor. "On model selection consistency of regularized M-estimators." Electron. J. Statist. 9 (1) 608 - 642, 2015. https://doi.org/10.1214/15-EJS1013
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