The Annals of Statistics

On the Nonparametric Estimation of Covariance Functions

Peter Hall, Nicholas I. Fisher, and Branka Hoffmann

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 22, Number 4 (1994), 2115-2134.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325774

Digital Object Identifier
doi:10.1214/aos/1176325774

Mathematical Reviews number (MathSciNet)
MR1329185

Zentralblatt MATH identifier
0828.62036

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G10: Hypothesis testing

Keywords
Convergence rate correlation covariance positive semidefinite stochastic process kernel variance variogram

Citation

Hall, Peter; Fisher, Nicholas I.; Hoffmann, Branka. On the Nonparametric Estimation of Covariance Functions. Ann. Statist. 22 (1994), no. 4, 2115--2134. doi:10.1214/aos/1176325774. https://projecteuclid.org/euclid.aos/1176325774


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