Abstract
First the minimum risk point estimation as well as the fixed-width confidence interval problems for the mean parameter of a linear process are addressed under the framework of Fakhre-Zakeri and Lee (1992). The accelerated versions of their full sequential methodologies are introduced in order to achieve operational savings. Next, multi-sample analogs are discussed along the lines of Mukhopadhyay and Sriram (1992) both under full sequential as well as accelerated sequential sampling. In either setup, the first-order asymptotic characteristics are highlighted.
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References
Chow YS, Robbins H (1965) On the asymptotic theory of fixed width sequential confidence intervals for the mean. Ann Math Statist 36:457–462
Chow YS, Yu KF (1981) The performance of a sequential procedure for the estimation of the mean. Ann Statist 9:184–189
Fakhre-Zakeri I, Lee S (1992) Sequential estimation of the mean of a linear process. Sequential Analysis 11:181–197
Ghosh M, Mukhopadhyay N (1979) Sequential point estimation of the mean when the distribution is unspecified. Commun Statist—Theory & Methods 8:637–651
Hall P (1983) Sequential estimation saving sampling operations. J Roy Statist Soc B, 45:219–223
Martinsek AT (1983) Second order approximation to the risk of a sequential procedure. Ann Statist 11:827–836
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 sequential estimation of a linear function of two means: The normal case. Metrika 24:197–201
Mukhopadhyay N (1993). An alternative formulation of accelerated sequential procedures with applications. Dept of Statist Tech Report No 93-27, Univ of Connecticut Storrs
Mukhopadhyay N, Solanky TKS (1991) Second order properties of accelerated stopping times with applications in sequential estimation. Sequential Analysis 10:99–123
Mukhopadhyay N, Sriram TN (1992) On sequential comparisons of means of first-order autoregressive models. Metrika 39:155–164
Robbins H (1959) Sequential estimation of the mean of a normal population. Prob & Statist Grenander U (eds.) 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
Woodroofe M (1977) Second order approximations for sequential point and interval estimation. Ann Statist 5:985–995
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Mukhopadhyay, N. Sequential estimation of means of linear processes. Metrika 42, 279–290 (1995). https://doi.org/10.1007/BF01894327
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DOI: https://doi.org/10.1007/BF01894327