A LOSS FUNCTION APPROACH TO MODEL SPECIFICATION TESTING AND ITS RELATIVE EFFICIENCY

• 成果类型: Article
• 署名作者: Hong, Yongmiao; Lee, Yoon-Jin
• 署名单位: Cornell University; Cornell University; Xiamen University; Xiamen University; Indiana University System; Indiana University Bloomington
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1099
• 发表日期: 2013
• 页码: 1166-1203
• 关键词: likelihood ratio tests; nonlinear time-series; Nonparametric Regression; CONDITIONAL HETEROSCEDASTICITY; bandwidth selection; maximum-likelihood; asymmetric loss; inferences; prediction; variance

摘要

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.