We introduce the Kernel-based Partial Conditional Mean Dependence, a scalar-valued measure of conditional mean dependence of
given
, while adjusting for the nonlinear dependence on
. Here
,
and
are random elements from arbitrary separable Hilbert spaces. This measure extends the Kernel-based Conditional Mean Dependence. As the estimator of the measure is developed, the concentration property of the estimator is proved. Numerical results demonstrate the effectiveness of the new dependence measure in the context of dependence testing, highlighting their advantages in capturing nonlinear partial conditional mean dependencies.
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