论文标题
本地固定过程的经验过程理论
Empirical process theory for locally stationary processes
论文作者
论文摘要
我们使用功能依赖度量为局部固定过程的经验过程理论提供了一个框架。我们的结果通过衡量依赖性并允许额外的时间依赖性的另一种常见可能性扩展了固定马尔可夫链和混合序列的已知结果。我们的主要结果是用于局部固定过程的功能性中心限制定理。此外，开发了最大的不平等现象。我们在某些示例中显示了我们的理论的适用性，例如，我们为非参数回归提供了均匀的收敛速率，并提供了局部固定的噪声。
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to measure dependence and allow for additional time dependence. Our main result is a functional central limit theorem for locally stationary processes. Moreover, maximal inequalities for expectations of sums are developed. We show the applicability of our theory in some examples, for instance we provide uniform convergence rates for nonparametric regression with locally stationary noise.
