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Kernel-Based Partial Conditional Mean Dependence
School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, China
School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, China
- 1 School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, China
- 2 School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, China
Open Journal of Statistics·Volume 15 (2025)·Pages 294–311·Published 9 June 2025·DOI10.4236/ojs.2025.153015
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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.
KeywordsPartial Conditional Mean DependenceHilbert SpaceHigh DimensionTest of Independence
- Cook, R.D. and Li, B. (2002) Dimension Reduction for Conditional Mean in Regression. The Annals of Statistics , 30, 455-474. https://doi.org/10.1214/aos/1021379861
- Williamson, B.D., Gilbert, P.B., Carone, M. and Simon, N. (2020) Nonparametric Variable Importance Assessment Using Machine Learning Techniques. Biometrics , 77, 9-22. https://doi.org/10.1111/biom.13392
- Dai, B., Shen, X. and Pan, W. (2024) Significance Tests of Feature Relevance for a Black-Box Learner. IEEE Transactions on Neural Networks and Learning Systems , 35, 1898-1911. https://doi.org/10.1109/tnnls.2022.3185742
- Williamson, B.D., Gilbert, P.B., Simon, N.R. and Carone, M. (2022) A General Framework for Inference on Algorithm-Agnostic Variable Importance. Journal of the American Statistical Association , 118, 1645-1658. https://doi.org/10.1080/01621459.2021.2003200
- Cai, L., Guo, X. and Zhong, W. (2024) Test and Measure for Partial Mean Dependence Based on Machine Learning Methods. Journal of the American Statistical Association , 120, 833-845. https://doi.org/10.1080/01621459.2024.2366030
- Welsh, A.H. and Yee, T.W. (2006) Local Regression for Vector Responses. Journal of Statistical Planning and Inference , 136, 3007-3031. https://doi.org/10.1016/j.jspi.2004.01.024
- Scheipl, F., Staicu, A. and Greven, S. (2015) Functional Additive Mixed Models. Journal of Computational and Graphical Statistics , 24, 477-501. https://doi.org/10.1080/10618600.2014.901914
- Sun, X., Du, P., Wang, X. and Ma, P. (2018) Optimal Penalized Function-on-Function Regression under a Reproducing Kernel Hilbert Space Framework. Journal of the American Statistical Association , 113, 1601-1611. https://doi.org/10.1080/01621459.2017.1356320
- Sun, Y. and Wang, Q. (2020) Function-on-Function Quadratic Regression Models. Computational Statistics & Data Analysis , 142, Article ID: 106814. https://doi.org/10.1016/j.csda.2019.106814
- Park, T., Shao, X. and Yao, S. (2015) Partial Martingale Difference Correlation. Electronic Journal of Statistics , 9, 1492-1517. https://doi.org/10.1214/15-ejs1047
- Shao, X. and Zhang, J. (2014) Martingale Difference Correlation and Its Use in High-Dimensional Variable Screening. Journal of the American Statistical Association , 109, 1302-1318. https://doi.org/10.1080/01621459.2014.887012
- Zhang, X., Yao, S. and Shao, X. (2018) Conditional Mean and Quantile Dependence Testing in High Dimension. The Annals of Statistics , 46, 219-246. https://doi.org/10.1214/17-aos1548