Abstract
The talk concerns sequential procedures detection of changes in linear relationship \({\rm{Y}_{k}(t)}\, = \, {\int^{1}_{0}}\,{\Psi}_{k}{\rm(t,\,s)}\,{\rm{X}_{k}(S){ds}}\,+\,{\varepsilon_{k}}{\rm\,(t)},\,{1}\,\leq\,{\rm\,{k}}< \infty\) between random functions Yk and Xk on [0,1], where errors { εk} [0,1] and { Ψk } are operators. Test procedures for testing the constancy of the operators Ψk ’s (i.e., Ψ1 = Ψ2 =…) against a change point alternative when a training sample is available is proposed and studied. The procedure utilizes the functional principal component analysis. Limit behavior of the developed test procedures are investigated.
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Aue, A., Hörmann, S., Horváth, L., Hušková, M. (2011). Sequential Stability Procedures for Functional Data Setups. In: Ferraty, F. (eds) Recent Advances in Functional Data Analysis and Related Topics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2736-1_6
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DOI: https://doi.org/10.1007/978-3-7908-2736-1_6
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