论文标题
一致的基于ICM的$χ^2 $规范测试
A Consistent ICM-based $χ^2$ Specification Test
论文作者
论文摘要
尽管综合条件力矩（ICM）规范测试具有综合性能，但由于测试的非客教性和可用的自举计划的高计算成本，它们并不常用于经验实践中。本文提出了基于一类称为广义的martingale差异差异（GMDD）的ICM指标类别的规范和平均独立性测试。提出的测试表现出一致性，渐近$χ^2 $ - 分布在原假设下以及计算效率。此外，它们表现出对未知形式的异性恋性的鲁棒性，并且可以适应以增强对特定替代方案的力量。还提供了使用Bahadur斜坡的基于经典的Bootstrap测试的功率比较。进行了蒙特卡洛模拟，以展示拟议的测试的出色尺寸控制和竞争力。
In spite of the omnibus property of Integrated Conditional Moment (ICM) specification tests, they are not commonly used in empirical practice owing to, e.g., the non-pivotality of the test and the high computational cost of available bootstrap schemes especially in large samples. This paper proposes specification and mean independence tests based on a class of ICM metrics termed the generalized martingale difference divergence (GMDD). The proposed tests exhibit consistency, asymptotic $χ^2$-distribution under the null hypothesis, and computational efficiency. Moreover, they demonstrate robustness to heteroskedasticity of unknown form and can be adapted to enhance power towards specific alternatives. A power comparison with classical bootstrap-based ICM tests using Bahadur slopes is also provided. Monte Carlo simulations are conducted to showcase the proposed tests' excellent size control and competitive power.
