Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 1 , pp. 128--143

COMPARING MEANS BY COMBINING INDIVIDUAL SEQUENTIAL ESTIMATORS AVAILABLE FROM INDEPENDENT STUDIES

By

NITIS MUKHOPADHYAY and SAIBAL CHATTOPADHYAY, *University of Connecticut*

SUMMARY. Suppose we have two independent normal populations having unknown means m _{1}, m _{2} and unknown variances. We also suppose we have available a stopping variable N_{i} and the associated sample mean from the i-th population, obtained in order to construct a fixed-width confidence interval for m _{i} only, i=1, 2. Under a fairly broad set of assumptions on N_{1} and N_{2}, we have provided the asymptotic second-order properties of a certain fixed-width confidance interval constructed for estimating m _{1}- m _{2}. Several examples have been included involving purely sequential, accelerated sequential and three stage sampling techniques. We have also remarked on the second-order characteristic of an associated point estimation problem.

*AMS (1980) subject classification.* 62L12,62F12.

*Key words and phrases.* Available individual estimators, followup sequential comparisons, second-order properties, fixed-width confidence intervals, point estimators, multistage sampling.

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