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On nonparametric spectral estimation

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Abstract

In this paper the Cramér-Rao bound (CRB) for a general nonparametric spectral estimation problem is derived under a local smoothness condition (more exactly, the spectrum is assumed to be well approximated by a piecewise constant function). Further-more, it is shown that under the aforementioned condition the Thomson method (TM) and Daniell method (DM) for power spectral density (PSD) estimation can be interpreted as approximations of the maximum likelihood PSD estimator. Finally the statistical efficiency of the TM and DM as nonparametric PSD estimators is examined and also compared to the CRB for autoregressive moving-average (ARMA)-based PSD estimation. In particular for broadband signals, the TM and DM almost achieve the derived nonparametric performance bound and can therefore be considered to be nearly optimal.

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Authors and Affiliations

  1. Department of Systems and Control, Uppsala University, P.O. Box 27, SE-75103, Uppsala, Sweden

    Petre Stoica & Tomas Sundin

Authors
  1. Petre Stoica
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  2. Tomas Sundin
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Additional information

This work was supported in part by the Swedish Foundation for Strategic Research (SSF) through the Senior Individual Grant Program.

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Stoica, P., Sundin, T. On nonparametric spectral estimation. Circuits Systems and Signal Process 18, 169–181 (1999). https://doi.org/10.1007/BF01206681

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