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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


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.


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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.


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

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

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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