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Uniform asymptotic normality of weighted sums of short-memory linear processes
Published online by Cambridge University Press: 04 May 2020
Abstract
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.
Keywords
MSC classification
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- © Applied Probability Trust 2020