Robust changepoint detection in the variability of multivariate functional data
arxiv(2021)
摘要
We consider the problem of robustly detecting changepoints in the variability
of a sequence of independent multivariate functions. We develop a novel
changepoint procedure, called the functional Kruskal–Wallis for covariance
(FKWC) changepoint procedure, based on rank statistics and multivariate
functional data depth. The FKWC changepoint procedure allows the user to test
for at most one changepoint (AMOC) or an epidemic period, or to estimate the
number and locations of an unknown amount of changepoints in the data. We show
that when the “signal-to-noise” ratio is bounded below, the changepoint
estimates produced by the FKWC procedure attain the minimax localization rate
for detecting general changes in distribution in the univariate setting
(Theorem 1). We also provide the behavior of the proposed test statistics for
the AMOC and epidemic setting under the null hypothesis (Theorem 2) and, as a
simple consequence of our main result, these tests are consistent (Corollary
1). In simulation, we show that our method is particularly robust when compared
to similar changepoint methods. We present an application of the FKWC procedure
to intraday asset returns and f-MRI scans. As a by-product of Theorem 1, we
provide a concentration result for integrated functional depth functions (Lemma
2), which may be of general interest.
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