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.

翻译：我们重新审视了比较回归函数这一经典问题，这是统计推断中的一个基本问题，对数据集成、迁移学习和因果推断等现代应用具有广泛意义。现有方法通常依赖于平滑技术，因此受到维度诅咒的限制。我们提出了一种基于核的条件均值依赖的广义概念，为回归函数相等的零假设提供了新的表征。基于这一重构，我们开发了两种新颖的检验方法，利用现代机器学习技术进行灵活估计。我们建立了检验统计量的渐近性质，这些性质在固定维度和高维情形下均成立。与现有方法通常需要严格分布假设不同，我们的框架仅施加温和的矩条件。通过大量数值研究证明了所提检验方法的有效性。