Jian Yan, Zhuoxi Li, Yang Ning, Yong Chen
arXiv 28 Oct 2025 · Statistics — Methodology
arXiv:2510.24714 · PDF · Extracted main text
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing approaches typically rely on smoothing techniques and are thus hindered by the curse of dimensionality. We propose a generalized notion of kernel-based conditional mean dependence that provides a new characterization of the null hypothesis of equal regression functions. Building on this reformulation, we develop two novel tests that leverage modern machine learning methods for flexible estimation. We establish the asymptotic properties of the test statistics, which hold under both fixed- and high-dimensional regimes. Unlike existing methods that often require restrictive distributional assumptions, our framework only imposes mild moment conditions. The efficacy of the proposed tests is demonstrated through extensive numerical studies.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Lai, T., Zhang, Z., and Wang, Y (2021) A kernel-based measure for conditional mean dependence | 0.811 | 4 | 2 | 100% |
| 2 | Li, R., Xu, K., Zhou, Y., and Zhu, L (2023) Testing the effects of high-dimensional covariates via aggregating cumulative covariances | 0.811 | 4 | 2 | 100% |
| 3 | Zhang, X., Yao, S., and Shao, X (2018) Conditional mean and quantile dependence testing in high dimension | 0.811 | 4 | 2 | 100% |
| 4 | Lavergne, P (2001) An equality test across nonparametric regressions | 0.737 | 3 | 2 | 100% |
| 5 | Dette, H. and Neumeyer, N (2001) Nonparametric analysis of covariance | 0.585 | 3 | 1 | 100% |
| 6 | He, C., Chen, C., and Zhu, L (2025) A goodness-of-fit assessment for general learning procedures in high dimensions | 0.585 | 3 | 1 | 100% |
| 7 | King, E., Hart, J. D., and Wehrly, T. E (1991) Testing the equality of two regression curves using linear smoothers | 0.585 | 3 | 1 | 100% |
| 8 | Neumeyer, N. and Dette, H (2003) Nonparametric comparison of regression curves: an empirical process approach | 0.585 | 3 | 1 | 100% |
| 9 | Pardo-Fernández, J. C., Van Keilegom, I., and González-Manteiga, W (2007) Testing for the equality of k regression curves | 0.585 | 3 | 1 | 100% |
| 10 | Pardo-Fernández, J. C., Jiménez-Gamero, M. D., and Ghouch, A. E (2015) A non-parametric anova-type test for regression curves based on characteristic functions | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 40 scored citations.