On sequential comparisons of means of first-order autoregressive models |
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Authors: | N Mukhopadhyay T N Sriram |
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Institution: | (1) Department of Statistics, University of Connecticut, 196 Auditorium Rd., 06269-3120 Storrs, CT, USA;(2) Department of Statistics, University of Georgia, 204 Statistics Building, 30602 Athens, Georgia, USA |
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Abstract: | The problem of estimating a linear combination,μ, of means ofp-independent, first-order autoregressive models is considered. Sequential procedures are derived (i) to estimateμ pointwise using the linear combination of sample means, subject to a loss function (squared error plus cost per observation),
and (ii) to arrive at a fixed-width confidence interval forμ. It is observed that in the case of point estimation we do not require a sampling scheme, where as in the case of interval
estimation we do require a sampling scheme and a scheme similar to the one given in Mukhopadhyay and Liberman (1989) is proposed.
All the first order efficiency properties of the sequential procedures involved here are derived. This paper is an extension
of results of Sriram (1987) involving one time series to multiple time series.
Research supported by AFOSR Grant number 89-0225. |
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Keywords: | Asymptotic risk efficiency asymptotic consistency asymptotic efficiency stopping rule sampling scheme |
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