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

作者：Hong Yongmiao^*; Lee Yoon Jin

来源：Annals of Statistics, 2013, 41(3): 1166-1203.

DOI：10.1214/13-AOS1099

• Efficiency
• generalized likelihood ratio test
• loss function
• local alternative
• kernel
• Pitman efficiency
• smoothing parameter

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.

• 出版日期2013-6
• 单位厦门大学