The nonparametric estimation of integrated diffusion processes has been extensively studied, with most existing research focusing on pointwise convergence. This paper is the first to establish uniform convergence rates for the Nadaraya-Watson estimators of their coefficients. We derive these rates over unbounded support under the assumptions of a vanishing observation interval and a long time horizon. Our findings serve as essential tools for specification testing and semiparametric inference in various diffusion models and time series, facilitating applications in finance, geology, and physics through nonparametric estimation methods.

翻译：积分扩散过程的非参数估计已被广泛研究，现有成果主要集中于逐点收敛性。本文首次建立了其系数Nadaraya-Watson估计量的一致收敛速率。在观测区间趋于零且时间跨度趋于无穷的假设条件下，我们在无界支撑集上推导出该速率。本研究结果为各类扩散模型与时间序列的设定检验及半参数推断提供了关键工具，通过非参数估计方法推动其在金融学、地质学与物理学等领域的应用。