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June, 1988 A Sieve Estimator for the Covariance of a Gaussian Process
Jay H. Beder
Ann. Statist. 16(2): 648-660 (June, 1988). DOI: 10.1214/aos/1176350825


Maximum likelihood estimation for the covariance $R$ of a zero-mean Gaussian process is considered, with no assumptions on the covariance or the "time" parameter set $T$. It is shown that the likelihood function is a.s. unbounded in general, and a sieve estimator $\hat{R}$ is constructed. The distribution of $\hat{R}$, considered as a process on $T \times T$, can be described exactly if a certain technical assumption is satisfied concerning the bivariate series expansion of $R$. It is then shown that $\hat{R}(s, t)$ is asymptotically unbiased and consistent (weakly and in mean square) at each $(s, t) \in T \times T$, and that $\hat{R}$ is strongly consistent (globally) in an appropriate norm.


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Jay H. Beder. "A Sieve Estimator for the Covariance of a Gaussian Process." Ann. Statist. 16 (2) 648 - 660, June, 1988.


Published: June, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0665.62089
MathSciNet: MR947567
Digital Object Identifier: 10.1214/aos/1176350825

Primary: 62M09
Secondary: 60G15, 60G30

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 2 • June, 1988
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