Consistently recovering the signal from noisy functional data

Siegfried Hörmann*, Fatima Jammoul

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In practice most functional data cannot be recorded on a continuum, but rather at discrete time points. It is also quite common that these measurements come with an additive error, which one would like eliminate for the statistical analysis. When the measurements for each functional datum are taken on the same grid, the underlying signal-plus-noise model can be viewed as a factor model. The signals refer to the common components of the factor model, the noise is related to the idiosyncratic components. We formulate a framework which allows to consistently recover the signal by a PCA based factor model estimation scheme. Our theoretical results hold under rather mild conditions, in particular we do not require specific smoothness assumptions for the underlying curves and allow for a certain degree of autocorrelation in the noise.

Original languageEnglish
Article number104886
JournalJournal of Multivariate Analysis
Volume189
DOIs
Publication statusPublished - May 2022

Keywords

  • Asymptotics
  • Factor models
  • Functional data
  • PCA
  • Preprocessing
  • Signal-plus-noise

ASJC Scopus subject areas

  • Numerical Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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