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

Sandberg, Johan LU and Sandsten, Maria LU (2011) In Eurasip Journal on Advances in Signal Processing
Abstract
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
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in
Eurasip Journal on Advances in Signal Processing
publisher
Hindawi Publishing Corporation
external identifiers
  • wos:000290383100001
  • scopus:79955015663
ISSN
1687-6172
DOI
10.1155/2011/140797
language
English
LU publication?
yes
id
6f455b2f-f104-4d9e-ad90-d46bdf199829 (old id 1987897)
date added to LUP
2011-06-29 08:38:08
date last changed
2017-03-13 13:12:14
@article{6f455b2f-f104-4d9e-ad90-d46bdf199829,
  abstract     = {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.},
  articleno    = {140797},
  author       = {Sandberg, Johan and Sandsten, Maria},
  issn         = {1687-6172},
  language     = {eng},
  publisher    = {Hindawi Publishing Corporation},
  series       = {Eurasip Journal on Advances in Signal Processing},
  title        = {Optimal Nonparametric Covariance Function Estimation for Any Family of Nonstationary Random Processes},
  url          = {http://dx.doi.org/10.1155/2011/140797},
  year         = {2011},
}