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June, 1983 Fixed Accuracy Estimation of an Autoregressive Parameter
T. L. Lai, D. Siegmund
Ann. Statist. 11(2): 478-485 (June, 1983). DOI: 10.1214/aos/1176346154


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 $|\beta| = 1$.


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T. L. Lai. D. Siegmund. "Fixed Accuracy Estimation of an Autoregressive Parameter." Ann. Statist. 11 (2) 478 - 485, June, 1983.


Published: June, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0519.62076
MathSciNet: MR696060
Digital Object Identifier: 10.1214/aos/1176346154

Primary: 62L10

Keywords: fixed width confidence interval , stopping rule , uniform asymptotic normality

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 2 • June, 1983
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