Open Access
Translator Disclaimer
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

Download Citation

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

Rights: Copyright © 1997 Institute of Mathematical Statistics

JOURNAL ARTICLE
37 PAGES


SHARE
Vol.25 • No. 5 • October 1997
Back to Top