2005/11/12 by Yuhong Yang · 10 citations
Mathematics · Engineering · #Statistical Methods and Inference #Control Systems and Identification #Statistical Methods and Bayesian Inference #Minimax #Model selection #Bayesian information criterion #Mathematics #Econometrics #Regression analysis #Regression #Bayesian inference #Selection (genetic algorithm) #Statistics #Function (biology) #Inference #Bayesian probability #Mathematical optimization #Computer science #Artificial intelligence
paper · doi:10.1093/biomet/92.4.937
openalex publication_date 2005/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
A traditional approach to statistical inference is to identify the true or best model first with little or no consideration of the specific goal of inference in the model identification stage. Can the pursuit of the true model also lead to optimal regression estimation? In model selection, it is well known that BIC is consistent in selecting the true model, and AIC is minimax-rate optimal for estimating the regression function. A recent promising direction is adaptive model selection, in which, in contrast to AIC and BIC, the penalty term is data-dependent. Some theoretical and empirical results have been obtained in support of adaptive model selection, but it is still not clear if it can really share the strengths of AIC and BIC. Model combining or averaging has attracted increasing attention as a means to overcome the model selection uncertainty. Can Bayesian model averaging be optimal for estimating the regression function in a minimax sense? We show that the answers to these questions are basically in the negative: for any model selection criterion to be consistent, it must behave suboptimally for estimating the regression function in terms of minimax rate of covergence; and Bayesian model averaging cannot be minimax-rate optimal for regression estimation.