Consistent model selection criteria on high dimensions

Authors:
Yongdai Kim;Sunghoon Kwon;Hosik Choi
Affiliations:
Department of Statistics, Seoul National University, Seoul, Korea;School of Statistics, University of Minnesota, Minneapolis, MN;Department of Informational Statistics, Hoseo University, Chungnam, Korea
Venue:
The Journal of Machine Learning Research
Year:
2012

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Abstract

Asymptotic properties of model selection criteria for high-dimensional regression models are studied where the dimension of covariates is much larger than the sample size. Several sufficient conditions for model selection consistency are provided. Non-Gaussian error distributions are considered and it is shown that the maximal number of covariates for model selection consistency depends on the tail behavior of the error distribution. Also, sufficient conditions for model selection consistency are given when the variance of the noise is neither known nor estimated consistently. Results of simulation studies as well as real data analysis are given to illustrate that finite sample performances of consistent model selection criteria can be quite different.