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We consider a sparse linear regression model, when the number of availablepredictors, $p$, is much larger than the sample size, $n$, and the number ofnon-zero coefficients, $p_0$, is small. To choose the regression model in thissituation, we cannot use classical model selection criteria. In recent years,special methods have been proposed to deal with this type of problem, forexample modified versions of Bayesian Information Criterion, like mBIC ormBIC2. It was shown that these criteria are consistent under the assumptionthat both $n$ and $p$ as well as $p_0$ tend to infinity and the error term isnormally distributed. In this article we prove the consistency of mBIC andmBIC2 under the assumption that the error term is a subgaussian randomvariable.

Consistency of modified versions of Bayesian Information Criterion in sparse linear regression with subgaussian errors