MAP model selection in Gaussian regression

Details MAP model selection in Gaussian regression MAP model selection in Gaussian regression

2009-12-22

arxiv.org/abs/0912.4387v3

Mathematics

Statistics Theory

22 pages

Scientific paper

We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized least squares estimation with a complexity penalty associated with a prior on the model size. We investigate the optimality properties of the resulting estimator. We establish the oracle inequality and specify conditions on the prior that imply its asymptotic minimaxity within a wide range of sparse and dense settings for "nearly-orthogonal" and "multicollinear" designs.

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