Finite sample effects in multichannel autoregressive modeling

Finite sample effects in multichannel autoregressive (AR) modeling are discussed. Finite sample effects are deviations from asymptotic behavior as a result of the fact that the number of estimated parameters is no longer small with respect to the number of observations. The order selected with the Akaike Information Criterion tends to be too high. This effect is called overfit. For multichannel signals, finite sample effects are an important cause of overfit. A consistent order selection criterion solves the problem of overfit at the expense of a high cost of underfit. Only by incorporating finite sample effects in the order selection criterion a satisfactory criterion can be found. The finite sample formulae in this paper provide a more accurate description of the behavior of AR estimators than asymptotic theory or the exact Cramer-Rao lower bound