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October 1996 Sequential estimation for the autocorrelations of linear processes
Sangyeol Lee
Ann. Statist. 24(5): 2233-2249 (October 1996). DOI: 10.1214/aos/1069362319


This paper considers sequential point estimation of the autocorrelations of stationary linear processes within the framework of the sequential procedure initiated by Robbins. The sequential estimator proposed here is based on the usual sample autocorrelations and is shown to be risk efficient in the sense of Starr as the cost per observation approaches zero. To achieve the asymptotic risk efficiency, we are led to study the uniform integrability and random central limit theorem of the sample autocorrelations. Some moment conditions are provided for the errors of the linear processes to establish the uniform integrability and random central limit theorem.


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Sangyeol Lee. "Sequential estimation for the autocorrelations of linear processes." Ann. Statist. 24 (5) 2233 - 2249, October 1996.


Published: October 1996
First available in Project Euclid: 20 November 2003

zbMATH: 0898.62099
MathSciNet: MR1421170
Digital Object Identifier: 10.1214/aos/1069362319

Primary: 62L12
Secondary: 60G40 , 62M10

Keywords: Asymptotic risk efficiency , linear processes , random central limit theorem , sample autocorrelations , sequential estimation , uniform integrability

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 5 • October 1996
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