A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE
提出一个基于加权Hellinger距离的非参数检验，用于检验条件独立性，在β混合条件下证明渐近正态性，蒙特卡洛模拟显示有限样本表现良好，并应用于汇率格兰杰非因果性检验。
We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f ( y | x , z ) and f ( y | x ), which is identically zero under the null. We use the functional delta method to expand the test statistic around the population value and establish asymptotic normality under β-mixing conditions. We show that the test is consistent and has power against alternatives at distance n −1/2 h − d /4 . The cases for which not all random variables of interest are continuously valued or observable are also discussed. Monte Carlo simulation results indicate that the test behaves reasonably well in finite samples and significantly outperforms some earlier tests for a variety of data generating processes. We apply our procedure to test for Granger noncausality in exchange rates.