Open Access
October 1997 On guaranteed estimation of the mean of an autoregressive process
V. Konev, S. Pergamenshchikov
Ann. Statist. 25(5): 2127-2163 (October 1997). DOI: 10.1214/aos/1069362391

Abstract

This paper considers the problem of sequential point estimation of the mean of a stable autoregressive process with unknown scale and autoregressive parameters. The construction of a sequential procedure makes use of special stopping rules and some modifications of least-squares estimates. The procedure enables estimating the mean with prescribed mean-square accuracy uniformly in nuisance parameters. The uniform asymptotic normality and the asymptotic minimaxity of the sequential estimate are established. The asymptotic formula for the mean sample size is obtained.

Citation

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V. Konev. S. Pergamenshchikov. "On guaranteed estimation of the mean of an autoregressive process." Ann. Statist. 25 (5) 2127 - 2163, October 1997. https://doi.org/10.1214/aos/1069362391

Information

Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0887.62087
MathSciNet: MR1474087
Digital Object Identifier: 10.1214/aos/1069362391

Subjects:
Primary: 62F12 , 62L12

Keywords: Autoregression , fixed-precision estimators , nuisance parameters , sequential estimation

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.25 • No. 5 • October 1997
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