Annals of Statistics

Fixed Accuracy Estimation of an Autoregressive Parameter

T. L. Lai and D. Siegmund

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Abstract

For a first order non-explosive autoregressive process with unknown parameter $\beta \in \lbrack -1, 1 \rbrack$, it is shown that if data are collected according to a particular stopping rule, the least squares estimator of $\beta$ is asymptotically normally distributed uniformly in $\beta$. In the case of normal residuals, the stopping rule may be interpreted as sampling until the observed Fisher information reaches a preassigned level. The situation is contrasted with the fixed sample size case, where the estimator has a non-normal unconditional limiting distribution when $|\beta| = 1$.

Article information

Source
Ann. Statist., Volume 11, Number 2 (1983), 478-485.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346154

Digital Object Identifier
doi:10.1214/aos/1176346154

Mathematical Reviews number (MathSciNet)
MR696060

Zentralblatt MATH identifier
0519.62076

JSTOR
links.jstor.org

Subjects
Primary: 62L10: Sequential analysis

Keywords
Stopping rule fixed width confidence interval uniform asymptotic normality

Citation

Lai, T. L.; Siegmund, D. Fixed Accuracy Estimation of an Autoregressive Parameter. Ann. Statist. 11 (1983), no. 2, 478--485. doi:10.1214/aos/1176346154. https://projecteuclid.org/euclid.aos/1176346154


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