Spectral-norm risk rates for multi-taper estimation of Gaussian processes

We consider the estimation of the covariance of a stationary Gaussian process on a multi-dimensional grid from observations taken on a general acquisition domain. We derive spectral-norm risk rates for multi-taper estimators. When applied to one-dimensional acquisition intervals, these show that Tho...

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Bibliographic Details
Published in:Journal of nonparametric statistics 2022-04, Vol.34 (2), p.448-464
Main Authors: Romero, José Luis, Speckbacher, Michael
Format: Article
Language:English
Subjects:
Domains
Estimators
Gaussian process
Minimax risk rates
multitaper estimators
Risk
spatiospectral concentration
spectral estimation
Tapering
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Summary:We consider the estimation of the covariance of a stationary Gaussian process on a multi-dimensional grid from observations taken on a general acquisition domain. We derive spectral-norm risk rates for multi-taper estimators. When applied to one-dimensional acquisition intervals, these show that Thomson's classical multi-taper has optimal risk rates, as they match known benchmarks. We also extend existing lower risk bounds to multi-dimensional grids and conclude that multi-taper estimators associated with certain two-dimensional acquisition domains also have almost optimal risk rates.
ISSN:1048-5252
1029-0311
DOI:10.1080/10485252.2022.2071888