Citation:
Anatolyev, Stanislav (2026) "AIC for many-regressor heteroskedastic regressions", Journal of Econometrics, vol. 256A, pp. 106270
Abstract:
The original and corrected Akaike information criteria (AIC) have been routinely used for model selection for ages. The penalty terms in these criteria are tied to the classical normal linear regression, characterized by conditional homoskedasticity and a small number of regressors relative to the sample size. We derive, from the same principles, a general version that takes account of conditional heteroskedasticity and regressor numerosity. The new AICm penalty takes a form of a ratio of certain weighted average error variances. The classical results on asymptotic prediction optimality of AIC are extended to AICm in heteroskedastic possibly misspecified models. Further, the infeasible AICm penalty can be operationalized via unbiased estimation of individual variances. Under suitable conditions, the feasible AICm criterion differs from the infeasible counterpart up to an asymptotically negligible term, and also possesses the property of asymptotic optimality. In simulations, the feasible AICm tends to select models that deliver systematically better out-of-sample predictions than the classical criteria. In the empirical application to an impact of legalized abortion on crime reduction, AICm tends to select a more parsimonious model than non-heteroskedasticity-robust versions of AIC.
Paper in RePEc:
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Presented at:
European Meeting of Statisticians 2026, Lugano, Switzerland, August 24-28, 2026
Erasmus University Rotterdam, Netherlands, March 19, 2026
26th International Conference on Computational Statistics, Giessen, Germany, August 27-30, 2024
Bernoulli-IMS 11th World Congress in Probability and Statistics, Bochum, Germany, August 12-16, 2024
11th Tartu Conference on Multivariate Statistics, Tartu, Estonia, June 25-28, 2024
Aarhus Workshop in Econometrics III, Aarhus University, Denmark, June 6-7, 2024