Properties of Algorithm 1 with AIC weights under KLIC ties

Establish coverage validity and asymptotic behavior of Algorithm 1 when smoothed AIC weights are used and multiple candidate models attain the minimal per-observation Kullback–Leibler information criterion, resulting in asymptotically random AIC weights.

Background

For smoothed information-criterion weighting in linear models, the authors derive convergence behaviors of AIC and BIC weights under stationarity: BIC concentrates on the most parsimonious KLIC minimizer(s), while AIC can yield random limiting weights if several models tie for the smallest KLIC.

They note that the usual assumptions ensuring convergence and local regularity may fail in this tie case for AIC, and explicitly state that the theoretical properties of their conformal model-averaging algorithm under such ties remain to be worked out.