Convergence rates of the generalized information criterion

Abstract

The generalized information criterion (GIC) selects a linear regression model by minimizing the sum of squared residuals plus a penalty parameter λ times a linear function of the model dimension. It is known that the GIC is asymptotically consistent in the sense that the error probability of selecting a non-optimal model by the GIC converges to zero when λ→∞ (as the sample size increases to ∞) at a certain rate. In the present paper we establish some convergence rates for the error probabilities of the GIC, in terms of λ and the order of the design matrix. The rates obtained here are sharper than the existing ones in the literature when the distribution of the response variable is non-normal. A discussion of the choice of the penalty parameter λ is also given.