Optimal Nonparametric Covariance Function Estimation for Any Family of Nonstationary Random Processes
(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:
https://lup.lub.lu.se/record/1987897
- author
- Sandberg, Johan LU and Sandsten, Maria LU
- organization
- publishing date
- 2011
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Eurasip Journal on Advances in Signal Processing
- article number
- 140797
- publisher
- Hindawi Limited
- 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
- 2016-04-01 14:45:56
- date last changed
- 2022-01-28 02:25:48
@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.}},
author = {{Sandberg, Johan and Sandsten, Maria}},
issn = {{1687-6172}},
language = {{eng}},
publisher = {{Hindawi Limited}},
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}},
doi = {{10.1155/2011/140797}},
year = {{2011}},
}