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February 1998 Adaptive covariance estimation of locally stationary processes
Stéphane Mallat, George Papanicolaou, Zhifeng Zhang
Ann. Statist. 26(1): 1-47 (February 1998). DOI: 10.1214/aos/1030563977

Abstract

It is shown that the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions. We model locally stationary processes with pseudo-differential operators that are time-varying convolutions. An adaptive covariance estimation is calculated by searching first for a "best" local cosine basis which approximates the covariance by a band or a diagonal matrix. The estimation is obtained from regularized versions of the diagonal coefficients in the best basis.

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Stéphane Mallat. George Papanicolaou. Zhifeng Zhang. "Adaptive covariance estimation of locally stationary processes." Ann. Statist. 26 (1) 1 - 47, February 1998. https://doi.org/10.1214/aos/1030563977

Information

Published: February 1998
First available in Project Euclid: 28 August 2002

zbMATH: 0949.62082
MathSciNet: MR1611808
Digital Object Identifier: 10.1214/aos/1030563977

Subjects:
Primary: 62M15
Secondary: 60G15

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 1 • February 1998
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