Adaptive inference for the mean of a gaussian process in functional data

Florentina Bunea, Andrada Ivanescu, Marten H. Wegkamp

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We propose and analyse fully data-driven methods for inference about the mean function of a Gaussian process from a sample of independent trajectories of the process, observed at random time points and corrupted by additive random error. Our methods are based on thresholded least squares estimators relative to an approximating function basis. The variable threshold levels are determined from the data and the resulting estimates adapt to the unknown sparsity of the mean function relative to the approximating basis. These results are obtained via novel oracle inequalities, which are further used to derive the rates of convergence of our mean estimates. In addition, we construct confidence balls that adapt to the unknown regularity of the mean and covariance function of the stochastic process. They are easy to compute since they do not require explicit estimation of the covariance operator of the process. A simulation study shows that the new method performs very well in practice and is robust against large variations that may be introduced by the random-error terms.

Original languageEnglish
Pages (from-to)531-538
Number of pages8
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume73
Issue number4
DOIs
StatePublished - 1 Sep 2011

Fingerprint

Functional Data
Gaussian Process
Random Error
Oracle Inequalities
Covariance Operator
Unknown
Covariance Function
Least Squares Estimator
Error term
Sparsity
Data-driven
Estimate
Confidence
Basis Functions
Stochastic Processes
Rate of Convergence
Ball
Regularity
Simulation Study
Trajectory

Keywords

  • Adaptive inference
  • Confidence balls
  • Functional data
  • Non-parametric mean estimation
  • Oracle inequalities
  • Stochastic processes
  • Thresholded estimators

Cite this

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Adaptive inference for the mean of a gaussian process in functional data. / Bunea, Florentina; Ivanescu, Andrada; Wegkamp, Marten H.

In: Journal of the Royal Statistical Society. Series B: Statistical Methodology, Vol. 73, No. 4, 01.09.2011, p. 531-538.

Research output: Contribution to journalArticle

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