## 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 language | English (US) |
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Pages (from-to) | 2865-2873 |

Number of pages | 9 |

Journal | IEEE Transactions on Signal Processing |

Volume | 54 |

Issue number | 8 |

DOIs | |

State | Published - 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