Detecting relevant changes in the spatiotemporal mean function

Holger Dette; Pascal Quanz

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arXiv · 2203.04716

Detecting relevant changes in the spatiotemporal mean function

Holger Dette·Pascal Quanz

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Abstract

For a spatiotemporal process $\{X_j(s,t) | ~s \in S~,~t \in T \}_{j =1, \ldots , n} $, where $S$ denotes the set of spatial locations and $T$ the time domain, we consider the problem of testing for a change in the sequence of mean functions. In contrast to most of the literature we are not interested in arbitrarily small changes, but only in changes with a norm exceeding a given threshold. Asymptotically distribution free tests are proposed, which do not require the estimation of the long-run spatiotemporal covariance structure. In particular we consider a fully functional approach and a test based on the cumulative sum paradigm, investigate the large sample properties of the corresponding test statistics and study their finite sample properties by means of simulation study.

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Holger Dette, Pascal Quanz. 2022-03-09. Detecting relevant changes in the spatiotemporal mean function. https://arxiv.org/abs/2203.04716

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