Minimax Adaptive Spectral Estimation From an Ensemble of Signals
- Resource Type
- Periodical
- Authors
- Bunea, F.; Ombao, H.; Auguste, A.
- Source
- IEEE Transactions on Signal Processing IEEE Trans. Signal Process. Signal Processing, IEEE Transactions on. 54(8):2865-2873 Aug, 2006
- Subject
- Signal Processing and Analysis
Communication, Networking and Broadcast Technologies
Computing and Processing
Minimax techniques
Signal processing
Random processes
Aggregates
Neuroscience
Electroencephalography
Frequency
Statistical analysis
Signal generators
Seismology
Curve aggregation
minimax estimation
model averaging
periodogram
risk bounds
spectrum
stationary random process
- Language
- ISSN
- 1053-587X
1941-0476
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^-2alpha /2alpha + 1$for spectra belonging to a generalized Lipschitz ball with smoothness index$alpha $. Our simulation study strongly suggests that our procedure works well in practice, and in a large variety of situations is preferable to the simple averaging of the$M$spectral estimates.