Model selection with data-oriented penalty

We consider the problem of model (or variable) selection in the classical regression model using the GIC (general information criterion), In this method the maximum likelihood is used with a penalty function denoted by C-n, depending on the sample size n and chosen to ensure consistency in the selection of the true model. There are various choices of C-n suggested in the literature on model selection. In this paper we show that a particular choice of C-n based on observed data, which makes it random, preserves the consistency property and provides improved performance over a fixed choice of C-n. (C) 1999 Elsevier Science B.V. All rights reserved.