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August 2011 Parametric or nonparametric? A parametricness index for model selection
Wei Liu, Yuhong Yang
Ann. Statist. 39(4): 2074-2102 (August 2011). DOI: 10.1214/11-AOS899

Abstract

In model selection literature, two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional (parametric scenario); Akaike’s information criterion (AIC) performs well in an asymptotic efficiency when the true model is infinite dimensional (nonparametric scenario). But there is little work that addresses if it is possible and how to detect the situation that a specific model selection problem is in. In this work, we differentiate the two scenarios theoretically under some conditions. We develop a measure, parametricness index (PI), to assess whether a model selected by a potentially consistent procedure can be practically treated as the true model, which also hints on AIC or BIC is better suited for the data for the goal of estimating the regression function. A consequence is that by switching between AIC and BIC based on the PI, the resulting regression estimator is simultaneously asymptotically efficient for both parametric and nonparametric scenarios. In addition, we systematically investigate the behaviors of PI in simulation and real data and show its usefulness.

Citation

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Wei Liu. Yuhong Yang. "Parametric or nonparametric? A parametricness index for model selection." Ann. Statist. 39 (4) 2074 - 2102, August 2011. https://doi.org/10.1214/11-AOS899

Information

Published: August 2011
First available in Project Euclid: 26 October 2011

zbMATH: 1227.62055
MathSciNet: MR2893862
Digital Object Identifier: 10.1214/11-AOS899

Subjects:
Primary: 62F12, 62J05
Secondary: 62J20

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 4 • August 2011
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