Detecting relevant changes in the spatiotemporal mean function

03/09/2022

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by   Holger Dette, et al.

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For a spatiotemporal process {X_j(s,t) |  s ∈ S , t ∈ T }_j =1, … , 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.