We propose an estimator of the kernel-based conditional mean dependence measure obtained from an appropriate modification of a naive estimator based on usual empirical estimators. We then get asymptotic normality of this estimator both under conditional mean independence hypothesis and under the alternative hypothesis. A new test for conditional mean independence of random variables valued into Hilbert spaces is then introduced.

翻译：我们提出一个基于内核的有条件平均依赖性措施的估算者,该措施来自根据通常的经验性估算者对天真的估算者进行适当修改的结果。 然后,我们在有条件平均独立假设和替代假设下,使该估算者无异于正常状态。 然后,对Hilbert空间中随机变量的有条件平均独立性进行了新的测试。