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Statistics Seminar Series
Thursday, Nov. 15, 2012, 4:00 PM
Cullimore, Room 111
New Jersey Institute of Technology
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Consistent
Cross-Validation for Tuning Parameter Selection in
High-Dimensional Variable Selection
Yang Feng
Department of Statistics, Columbia University
Abstract
For variable selection in high dimensional
setting, we systematically investigate the
properties of several cross-validation methods
for selecting the penalty parameter in the popular penalized maximum likelihood method. We show that the popular
leave-one-out cross-validation and K-fold
cross-validation (with any pre-specified value
of K) are both inconsistent in terms of model selection. A new cross-validation procedure, Consistent Cross-Validation
(CCV) is proposed. Under certain technical
conditions, CCV is shown to enjoy the model
selection consistency property. Extensive simulations and real data analysis are conducted, supporting the
theoretical results.