论文标题
任何时间在Model-X下的有条件独立性的有效测试
Anytime Valid Tests of Conditional Independence Under Model-X
论文作者
论文摘要
我们提出了一种顺序的，随时随地的valid方法，以测试响应$ y $的条件独立性和一个预测因子$ x $给定随机向量$ z $。拟议的测试基于电子统计量和测试martingales，该测试概括了似然比并允许在任意停止时间时有效推断。根据最近引入的Model-X设置，我们的测试取决于给定$ z $的条件分布的可用性，或者至少具有足够尖锐的近似值。在这种情况下，我们得出了一种构建用于测试条件独立性的电子统计量的通用方法，表明它导致了简单替代方案的增长率最佳电子统计量，并证明我们的方法在逻辑回归模型的特殊情况下用渐近功率构建了测试。进行仿真研究是为了证明与已建立的顺序测试方法相比，该方法在功率方面具有竞争力，并且在违反模型-X假设方面具有鲁棒性。
We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood ratios and allow valid inference at arbitrary stopping times. In accordance with the recently introduced model-X setting, our test depends on the availability of the conditional distribution of $X$ given $Z$, or at least a sufficiently sharp approximation thereof. Within this setting, we derive a general method for constructing e-statistics for testing conditional independence, show that it leads to growth-rate optimal e-statistics for simple alternatives, and prove that our method yields tests with asymptotic power one in the special case of a logistic regression model. A simulation study is done to demonstrate that the approach is competitive in terms of power when compared to established sequential and nonsequential testing methods, and robust with respect to violations of the model-X assumption.
