The Annals of Statistics

Monotone spectral density estimation

Dragi Anevski and Philippe Soulier

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We propose two estimators of a monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.

Article information

Ann. Statist., Volume 39, Number 1 (2011), 418-438.

First available in Project Euclid: 15 February 2011

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Zentralblatt MATH identifier

Primary: 62E20: Asymptotic distribution theory 62G05: Estimation 62M15: Spectral analysis

Limit distributions spectral density estimation monotone long-range dependence Gaussian process linear process


Anevski, Dragi; Soulier, Philippe. Monotone spectral density estimation. Ann. Statist. 39 (2011), no. 1, 418--438. doi:10.1214/10-AOS804.

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