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March, 1987 A Sieve Estimator for the Mean of a Gaussian Process
Jay H. Beder
Ann. Statist. 15(1): 59-78 (March, 1987). DOI: 10.1214/aos/1176350253

Abstract

A new sieve estimator for the mean function $m(t)$ of a general Gaussian process of known covariance is presented. The estimator $\hat{m}(t)$ is given explicitly from the data and has a simple distribution. It is shown that $\hat{m}(t)$ is asymptotically unbiased and consistent (weakly and in mean square) at each $t$, and that $\hat{m}$ is strongly consistent for $m$ in an appropriate norm. No assumptions are made about the "time" parameter or the covariance.

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Jay H. Beder. "A Sieve Estimator for the Mean of a Gaussian Process." Ann. Statist. 15 (1) 59 - 78, March, 1987. https://doi.org/10.1214/aos/1176350253

Information

Published: March, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0619.62078
MathSciNet: MR885724
Digital Object Identifier: 10.1214/aos/1176350253

Subjects:
Primary: 62M09
Secondary: 60G15, 60G30

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 1 • March, 1987
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