Optimal Nonparametric Covariance Function Estimation for Any Family of Nonstationary Random Processes. (9th January 2011)

• Record Type: Journal Article
• Authors: Sandberg Sandberg, Johan Johan; Hansson-Sandsten Hansson-Sandsten, Maria Maria
• Other Names: Napolitano Napolitano Antonio Antonio Academic Editor.
• Is Part Of: EURASIP journal on advances in signal processing. Volume 2011(2011)
• Publication Date: 2011-01-09
• Subjects: Signal processing -- Periodicals; Traitement du signal; Signal processing; Periodicals; 621.3822
• DOI: 10.1155/2011/140797
• Languages: English
• ISSNs: 1687-6172

Abstract

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.