Sequential Stability Procedures for Functional Data Setups

  • Alexander Aue
  • Siegfried Hörmann
  • Lajos Horváth
  • Marie Hušková
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Alexander Aue
    • 1
  • Siegfried Hörmann
    • 2
  • Lajos Horváth
    • 3
  • Marie Hušková
    • 4
  1. 1.University of CaliforniaDavisUSA
  2. 2.UniversitéLibre de BruxellesBrusselsBelgium
  3. 3.University of UtahSalt Lake CityUSA
  4. 4.Charles University of PraguePragueCzech Republic

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