A nonparametric Hellinger metric test for conditional independence
A nonparametric Hellinger metric test for conditional independence
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DOI：
10.1017/s0266466608080341
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发表时间：
2008-08-01
影响因子：
0.8
通讯作者：
White, Halbert
中科院分区：
文献类型：
--
作者：
Su, Liangjun;White, Halbert
基于两个条件密度f(y垂直杆x，z)和f(y垂直杆x)之间的加权Hellinger距离，我们提出了条件独立性的非参数检验，在零点下f(y垂直杆x，z)恒定为零。我们使用函数Delta方法将检验统计量扩展到总体值附近，并在贝塔混合条件下建立了渐近正态分布。我们证明了在距离n(-1/2)h(-d/4)时，该检验是相容的，并且相对于备选方案具有能力。还讨论了不是所有感兴趣的随机变量都是连续取值或可观测的情况。蒙特卡罗模拟结果表明，该测试在有限样本中表现得相当好，并且在各种数据生成过程中的表现明显优于以前的一些测试。我们应用我们的程序来检验汇率中的格兰杰非因果关系。
We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f(y vertical bar x, z) and f(y vertical bar 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 beta-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.