TITLE:
Kernel-Based Partial Conditional Mean Dependence
AUTHORS:
Zhentao Tian, Zhongzhan Zhang
KEYWORDS:
Partial Conditional Mean Dependence, Hilbert Space, High Dimension, Test of Independence
JOURNAL NAME:
Open Journal of Statistics,
Vol.15 No.3,
June
23,
2025
ABSTRACT: We introduce the Kernel-based Partial Conditional Mean Dependence, a scalar-valued measure of conditional mean dependence of
Y
given
X
, while adjusting for the nonlinear dependence on
Z
. Here
X
,
Y
and
Z
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.