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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 32, Fasc. 1,
pages 47 - 55
 

WEAK CONSISTENCY OF MODIFIED VERSIONS OF BAYESIAN INFORMATION CRITERION IN A SPARSE LINEAR REGRESSION

Piotr Szulc

Abstract: We consider the regression model in the situation when the number of available regressors p n is much bigger than the sample size n and the number of nonzero coefficients p 0n is small (the sparse regression). To choose the regression model, we need to identify the nonzero coefficients. However, in this situation the classical model selection criteria for the choice of predictors like, e.g., the Bayesian Information Criterion (BIC) overestimate the number of regressors. To address this problem, several modifications of BIC have been recently proposed. In this paper we prove weak consistency of some of these modifications under the assumption that both n and p n as well as p 0n go to infinity.

2000 AMS Mathematics Subject Classification: Primary: 62J05; Secondary: 92D20.

Keywords and phrases: Sparse linear regression, mBIC, mBIC2, consistency.

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