Detection of change in the spatiotemporal mean function. (17th February 2016)

• Record Type: Journal Article
• Authors: Gromenko, Oleksandr; Kokoszka, Piotr; Reimherr, Matthew
• Is Part Of: Journal of the Royal Statistical Society. Volume 79:Number 1(2017)
• Page Start: 29
• Page End: 50
• Publication Date: 2016-02-17
• Subjects: Change point -- Functional data -- Mean function -- Spatiotemporal data; Statistics -- Periodicals; Great Britain -- Statistics -- Periodicals; 519.2
• DOI: 10.1111/rssb.12156
• Languages: English
• ISSNs: 1369-7412

Abstract

Summary: The paper develops inferential methodology for detecting a change in the annual pattern of an environmental variable measured at fixed locations in a spatial region. Using a framework built on functional data analysis, we model observations as a collection of function‐valued time sequences available at many sites. Each sequence is modelled as an annual mean function, which may change, plus a sequence of error functions, which are spatially correlated. The tests statistics extend the cumulative sum paradigm to this more complex setting. Their asymptotic distributions are not parameter free because of the spatial dependence but can be effectively approximated by Monte Carlo simulations. The new methodology is applied to precipitation data. Its finite sample performance is assessed by a simulation study.