We establish a strong Gaussian approximation for high-dimensional non-degenerate U-statistics with diverging dimension. Under mild assumptions, we construct, on a sufficiently rich probability space, a Gaussian process that uniformly approximates the entire sequential U-statistic process. The approximation error is explicitly characterized and vanishes under polynomial growth of the dimension. The key technical contribution is a sharp martingale maximal inequality for completely degenerate U-statistics, combined with a high-dimensional strong approximation for independent sums. This coupling yields functional Gaussian limits without relying on $\mathcal{L}^\infty$-type bounds or bootstrap arguments. The theory is illustrated through three representative examples of U-statistics: the spatial Kendall's tau matrix, the multivariate Gini's mean difference, and the characteristic dispersion parameter. As applications, we derive Brownian bridge approximations for U-statistic-based change-point statistics and develop a self-normalized relevant testing procedure whose limiting distribution is fully pivotal. The framework naturally accommodates bounded kernels and therefore remains valid under heavy-tailed distributions. Overall, our results provide a unified probability-theoretic foundation for high-dimensional inference based on U-statistics.

翻译：本文为发散维度下的高维非退化U统计量建立了强高斯逼近理论。在温和假设下，我们在足够丰富的概率空间上构造了一个高斯过程，该过程能一致逼近整个序列U统计量过程。逼近误差被显式刻画，并在维度多项式增长条件下趋于零。关键的技术贡献在于：针对完全退化U统计量提出了尖锐的鞅型极大值不等式，并结合独立和的高维强逼近方法。该耦合方法无需依赖$\mathcal{L}^\infty$型边界或自助法论证即可获得泛函高斯极限。理论通过三类代表性U统计量实例得到阐释：空间Kendall's tau矩阵、多元Gini均值差以及特征离散参数。作为应用，我们推导了基于U统计量的变点统计量的布朗桥逼近，并发展了一种自标准化相关检验程序，其极限分布完全具有枢轴性。该框架天然适用于有界核函数，因此在重尾分布下依然有效。总体而言，我们的研究结果为基于U统计量的高维推断提供了统一的概率论基础。