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December, 1994 On the Nonparametric Estimation of Covariance Functions
Peter Hall, Nicholas I. Fisher, Branka Hoffmann
Ann. Statist. 22(4): 2115-2134 (December, 1994). DOI: 10.1214/aos/1176325774


We describe kernel methods for estimating the covariance function of a stationary stochastic process, and show how to ensure that the estimator has the positive semidefiniteness property. From a practical viewpoint, our method is significant because it does not demand a parametric model for covariance. From a technical angle, our results exhibit a striking departure from those in more familiar cases of kernel estimation. For example, in the context of covariance estimation, kernel estimators can have the same convergence rates as maximum likelihood estimators, and can have exceptionally fast convergence rates when employed to estimate variance.


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Peter Hall. Nicholas I. Fisher. Branka Hoffmann. "On the Nonparametric Estimation of Covariance Functions." Ann. Statist. 22 (4) 2115 - 2134, December, 1994.


Published: December, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0828.62036
MathSciNet: MR1329185
Digital Object Identifier: 10.1214/aos/1176325774

Primary: 62G05
Secondary: 62G10

Keywords: convergence rate , Correlation , Covariance , ‎kernel‎ , positive semidefinite , stochastic process , variance , variogram

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 4 • December, 1994
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