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.
@article{1069362391,
author = {Konev, V. and Pergamenshchikov, S.},
title = {On guaranteed estimation of the mean of an autoregressive process},
journal = {Ann. Statist.},
volume = {25},
number = {6},
year = {1997},
pages = { 2127-2163},
language = {en},
url = {http://dml.mathdoc.fr/item/1069362391}
}
Konev, V.; Pergamenshchikov, S. On guaranteed estimation of the mean of an autoregressive process. Ann. Statist., Tome 25 (1997) no. 6, pp. 2127-2163. http://gdmltest.u-ga.fr/item/1069362391/