Sequential estimation for dependent observations with an application to non-standard autoregressive processes

I.V. Basawa, W.P. McCormick and T.N. Sriram

Stochastic Processes and their Applications, 1990, vol. 35, issue 1, 149-168

Abstract: This paper is concerned with a general approach for sequential estimation for dependent observations, and an application to a non-standard first order autoregressive process having Weibull errors. The natural estimator of the autoregressive parameter when the errors are non negative turns out to be an extreme value estimator. The least squares estimator serves as an alternative to the extreme value estimator. For fully sequential sampling schemes, the asymptotic risk accuracy of the extreme value estimator and the least squares estimator are established. Furthermore, when the errors are exponentially distributed it is shown that (asymptotically) the expected sample size corresponding to the extreme value estimator differs from the best fixed sample size (in absolute value) by at most 1 unit. Finally, the efficiencies of the two competing sequential estimators are computed for different values of the index of the Weibull distribution.

Keywords: extreme; value; estimator; stopping; time; asymptotic; risk; accuracy; asymptotic; relative; efficiency; reverse; submartingale; uniform; integrability (search for similar items in EconPapers)
Date: 1990
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