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Optimal Nonparametric Covariance Function Estimation for Any Family of Nonstationary Random Processes

Publiceringsår: 2011
Språk: Engelska
Publikation/Tidskrift/Serie: Eurasip Journal on Advances in Signal Processing
Dokumenttyp: Artikel i tidskrift
Förlag: Hindawi Publishing Corporation


A covariance function estimate of a zero-mean nonstationary random process in discrete time is accomplished from one observed realization by weighting observations with a kernel function. Several kernel functions have been proposed in the literature. In this paper, we prove that the mean square error (MSE) optimal kernel function for any parameterized family of random processes can be computed as the solution to a system of linear equations. Even though the resulting kernel is optimized for members of the chosen family, it seems to be robust in the sense that it is often close to optimal for many other random processes as well. We also investigate a few examples of families, including a family of locally stationary processes, nonstationary AR-processes, and chirp processes, and their respective MSE optimal kernel functions.


  • Probability Theory and Statistics


  • Statistical Signal Processing-lup-obsolete
  • Stochastics in Medicine-lup-obsolete
  • Statistical Signal Processing Group
  • ISSN: 1687-6172

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