Let $X_1, X_2,\dots$ be a short-memory linear process of random variables. For $1\leq q<2$ , let ${\mathcal{F}}$ be a bounded set of real-valued functions on [0, 1] with finite q-variation. It is proved that $\{n^{-1/2}\sum_{i=1}^nX_i\,f(i/n)\colon f\in{\mathcal{F}}\}$ converges in outer distribution in the Banach space of bounded functions on ${\mathcal{F}}$ as $n\to\infty$ . Several applications to a regression model and a multiple change point model are given.

中文翻译：

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短记忆线性过程的加权和的一致渐近正态性

让$X_1, X_2,\点$是随机变量的短记忆线性过程。为了$1\leq q<2$， 让${\mathcal{F}}$是 [0, 1] 上的一组有界实值函数，具有有限q-变化。证明了$\{n^{-1/2}\sum_{i=1}^nX_i\,f(i/n)\冒号 f\in{\mathcal{F}}\}$在有界函数的 Banach 空间中收敛于外部分布${\mathcal{F}}$作为$n\to\infty$. 给出了回归模型和多变化点模型的几种应用。