CONVERGENCE-RATES OF THE GENERALIZED INFORMATION CRITERION

The generalized information criterion (GIC) selects a linear regressio n model by minimizing the sum of squared residuals plus a penalty para meter lambda times a linear function of the model dimension. It is kno wn that the GIC is asymptotically consistent in the sense that the err or probability of selecting a non-optimal model by the GIC converges t o zero when lambda --> infinity (as the sample size increases to infin ity) at a certain rate, In the present paper we establish some converg ence rates fbr the error probabilities of the GIC, in terms of lambda and the order of the design matrix. The rates obtained here are sharpe r than the existing ones in the literature when the distribution of th e response variable is nonnormal. A discussion of the choice of the pe nalty parameter lambda is also given.