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June 2013 A loss function approach to model specification testing and its relative efficiency
Yongmiao Hong, Yoon-Jin Lee
Ann. Statist. 41(3): 1166-1203 (June 2013). DOI: 10.1214/13-AOS1099

Abstract

The generalized likelihood ratio (GLR) test proposed by Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153–193] and Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer] is a generally applicable nonparametric inference procedure. In this paper, we show that although it inherits many advantages of the parametric maximum likelihood ratio (LR) test, the GLR test does not have the optimal power property. We propose a generally applicable test based on loss functions, which measure discrepancies between the null and nonparametric alternative models and are more relevant to decision-making under uncertainty. The new test is asymptotically more powerful than the GLR test in terms of Pitman’s efficiency criterion. This efficiency gain holds no matter what smoothing parameter and kernel function are used and even when the true likelihood function is available for the GLR test.

Citation

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Yongmiao Hong. Yoon-Jin Lee. "A loss function approach to model specification testing and its relative efficiency." Ann. Statist. 41 (3) 1166 - 1203, June 2013. https://doi.org/10.1214/13-AOS1099

Information

Published: June 2013
First available in Project Euclid: 13 June 2013

zbMATH: 1293.62100
MathSciNet: MR3113807
Digital Object Identifier: 10.1214/13-AOS1099

Subjects:
Primary: 62G10

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 3 • June 2013
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