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Gretton, A., Bousquet, O., Smola, A. and Schölkopf, B. (2005) Measuring Statistical Dependence with Hilbert-Schmidt Norms. In: Jain, S., Simon, H.U. and Tomita, E., Eds., Lecture Notes in Computer Science, Springer, 63-77.
https://doi.org/10.1007/11564089_7

has been cited by the following article:

• 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.