In this article, we propose an adaptive-to-model test for conditional independence through groupwise dimension reduction developed in sufficient dimension reduction field. The test statistic under the null hypothesis is asymptotically normally distributed. Although it is also based on nonparametric estimation like any local smoothing tests for conditional independence, its behavior is similar to existing local smoothing tests with only the number of covariates under the null hypothesis. Furthermore, it can detect local alternatives distinct from the null at the rate that is also only related to the number of covariates under the null hypothesis. Therefore, the curse of dimensionality is largely alleviated. To achieve the above goal, we also suggest a groupwise least squares estimation for the groupwise central subspace in sufficient dimension reduction. It is of its own importance in estimation theory though it is as a by-product for the model adaptation of test statistic described herewith. Numerical studies and analyses for two real data sets are then conducted to examine the finite sample performance of the proposed test.

中文翻译：

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条件独立性测试：基于分组降维的模型自适应方法

在本文中，我们通过在足够的降维领域中开发的分组降维，提出了一种对条件独立性的自适应模型测试。原假设下的检验统计量呈渐近正态分布。尽管它也像条件独立性的任何局部平滑检验一样基于非参数估计，但其行为类似于现有的局部平滑检验，只有在原假设下协变量的数量。此外，它可以以同样仅与零假设下的协变量数量相关的速率检测与零不同的局部替代方案。因此，维数灾难在很大程度上得到了缓解。为实现上述目标，我们还建议在充分降维的情况下对分组中心子空间进行分组最小二乘估计。尽管它是本文描述的检验统计量的模型适应的副产品，但它在估计理论中具有其自身的重要性。然后对两个真实数据集进行数值研究和分析，以检查所提议测试的有限样本性能。