Minimax adaptive spectral estimation from an ensemble of signals

Florentina Bunea*, Hernando Ombao, Anna Auguste

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We develop a statistical method for estimating the spectrum from a data set that consists of several signals, all of which are realizations of a common random process. We first find estimates of the common spectrum using each signal; then we construct M partial aggregates. Each partial aggregate is a linear combination of M - 1 of the spectral estimates. The weights are obtained from the data via a least squares criterion. The final spectral estimate is the average of these M partial aggregates. We show that our final estimator is minimax rate adaptive if at least two of the estimators per signal attain the optimal rate N-2a/sa+1 for spectra belonging to a generalized Lipschitz ball with smoothness index α. Our simulation study strongly suggests that our procedure works well in practice, and in a large variety of situations is preferable to the simple averaging of the M spectral estimates.

Original languageEnglish (US)
Pages (from-to)2865-2873
Number of pages9
JournalIEEE Transactions on Signal Processing
Volume54
Issue number8
DOIs
StatePublished - Aug 1 2006

Keywords

  • Curve aggregation
  • Minimax estimation
  • Model averaging
  • Periodogram
  • Risk bounds
  • Spectrum
  • Stationary random process

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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