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.
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Chow YS, Robbins HE (1965) On the Asymptotic Theory of Fixed Width Sequential Confidence Intervals for the Mean. Ann Math Statist 36:457–462
Mukhopadhyay N (1976) Sequential Estimation of a Linear Function of Means of Three Normal Populations. J Amer Statist Assoc 71:149–153
Mukhopadhyay N (1977) Remarks on a Sequential Estimation of a Linear Function of Two Means: The Normal Case. Metrika 24:197–201
Mukhopadhyay N (1991) Parametric Sequential Point Estimation. In: Ghosh BK, Sen PK (Eds) Handbook of Sequential Analysis, Chapter 10, 245–267. Marcel Dekker Inc, New York
Mukhopadhyay N, Liberman S (1989) Sequential Estimation of a Linear Function of Mean Vectors. Sequential Analysis 8:381–394
Robbins HE (1959) Sequential Estimation of the Mean of a Normal Population. In: Grenander U (Ed) Probability and Statistics. Wiley, New York, pp 235–245
Robbins H, Simons G, Starr N (1967) A Sequential Analogue of the Behrens-Fisher Problem. Ann Math Statist 38:1384–1391
Sriram TN (1987) Sequential Estimation of the Mean of a First-Order Stationary Autoregressive Process. Ann Statist 15:1079–1090
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Research supported by AFOSR Grant number 89-0225.
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Mukhopadhyay, N., Sriram, T.N. On sequential comparisons of means of first-order autoregressive models. Metrika 39, 155–164 (1992). https://doi.org/10.1007/BF02613995
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DOI: https://doi.org/10.1007/BF02613995