AI 中文总结
本研究提出二次型统计量的随机不变性测试方法，改进了自相关检验的非参数变体，功效优于经典检验，可适配其他二次型统计量。
AI 中文摘要
置换随机化检验是假设检验中极为常用的非参数方法，但随机化检验也可通过随机旋转等其他群变换实现。本研究在具有闭式p值的统一框架下，探讨二次型统计量的不变性问题，特别针对时间序列数据任意滞后阶数的自相关检验，提出经典Durbin-Watson检验的非参数变体。该检验通过对检验统计量的一组不变性群进行积分来执行，基于紧群上的集中不等式，可逐阶推导易于计算的p值解析公式，从而无需常规的大规模蒙特卡洛模拟。在模拟数据中，所提检验在识别显著自相关的统计功效上优于经典Breusch-Godfrey检验和Ljung-Box检验；还可用于识别大滞后阶数的自相关，如遵循约11年（132个月）周期的月度太阳强度数据。该方法的通用形式可轻松适配其他二次型统计量。
英文摘要
Randomization testing with permutations is a very common nonparametric approach to hypothesis testing. However, randomization testing can be done with other group transformations including random rotations. In this work, we consider the problem of invariance in quadratic form statistics under a unified framework with closed form p-values. In particular, we propose a nonparametric variant of the classic Durbin-Watson test for testing for autocorrelation in time series data at arbitrary lags. Our test is performed by integrating over a group of invariances of the test statistic, and easy-to-compute analytic formulae for the p-value are derived from concentration inequalities on compact groups on a per-lag basis. Thus, the usual necessity of large-scale Monte Carlo simulations is rendered unnecessary. Our tests outperform the classic Breusch-Godfrey and Ljung-Box tests on simulated data with respect to statistical power to identify significant autocorrelation. They also can be used to identify the presence of autocorrelation at large lags such as in monthly solar intensity data, which follows an approximate 11 year (132 month) cycle. The general formulation of this approach can be easily adapted to other quadratic form statistics.
Comments26 pages, 9 figures, 2 tables
