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September, 1975 Asymptotically Efficient Estimators for a Constant Regression with Vector- Valued Stationary Residuals
Rolf K. Adenstedt
Ann. Statist. 3(5): 1109-1121 (September, 1975). DOI: 10.1214/aos/1176343243

Abstract

Estimation of linear functions of a vector parameter $\theta$ when an observed discrete- or continuous-time vector-valued stationary process has mean value $H\theta, H$ a known matrix, is considered. Large-sample comparisons of best linear unbiased estimators and estimators based on the sample mean are made. Limits and rates of convergence of the variances of these estimators are obtained. It is shown that under general conditions there are asymptotically efficient estimators based on the sample mean, their form determined by the spectrum at the origin. Conditions under which all least squares estimators are asymptotically efficient are also given.

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Rolf K. Adenstedt. "Asymptotically Efficient Estimators for a Constant Regression with Vector- Valued Stationary Residuals." Ann. Statist. 3 (5) 1109 - 1121, September, 1975. https://doi.org/10.1214/aos/1176343243

Information

Published: September, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0318.62046
MathSciNet: MR375697
Digital Object Identifier: 10.1214/aos/1176343243

Subjects:
Primary: 62M10
Secondary: 62J05

Keywords: Asymptotic efficiency , linear estimation , Moore-Penrose pseudoinverse , regression , spectral representations , stationary vector-valued processes

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 5 • September, 1975
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