The Annals of Statistics

Adaptive covariance estimation of locally stationary processes

Stéphane Mallat, George Papanicolaou, and Zhifeng Zhang

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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.

Article information

Ann. Statist., Volume 26, Number 1 (1998), 1-47.

First available in Project Euclid: 28 August 2002

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Zentralblatt MATH identifier

Primary: 62M15: Spectral analysis
Secondary: 60G15: Gaussian processes

Locally stationary processes local cosine bases adaptive covariance estimation approximate Karhunen-Loeve basis


Mallat, Stéphane; Papanicolaou, George; Zhang, Zhifeng. Adaptive covariance estimation of locally stationary processes. Ann. Statist. 26 (1998), no. 1, 1--47. doi:10.1214/aos/1030563977.

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