On the Weak Convergence of the Function-Indexed Sequential Empirical Process and its Smoothed Analogue under Nonstationarity
非平稳条件下函数索引序贯经验过程及其平滑版本的弱收敛
We study the sequential empirical process indexed by general function classes and its smoothed set-indexed analogue. Sufficient conditions for asymptotic equicontinuity are provided for nonstationary arrays of time series. This yields comprehensive general results that are applicable to various notions of dependence, which is exemplified in detail for nonstationary $α$-mixing series. Especially, we obtain the weak convergence of the sequential process under essentially the…