Date of this Version
The Annals of Statistics
Consider the problem of estimating a common mean of two independent normal distributions, each with unknown variances. Note that the problem of recovery of interblock information in balanced incomplete blocks designs is such a problem. Suppose a random sample of size m is drawn from the first population and a random sample of size n is drawn from the second population. We first show that the sample mean of the first population can be improved on (with an unbiased estimator having smaller variance), provided m ≧ 2 and n ≧ 3. The method of proof is applicable to the recovery of information problem. For that problem, it is shown that interblock information could be used provided b ≧ 4. Furthermore for the case b = t = 3, or in the common mean problem, where n = 2, it is shown that the prescribed estimator does not offer improvement. Some of the results for the common mean problem are extended to the case of K means. Results similar to some of those obtained for point estimation, are also obtained for confidence estimation.
common mean, unbiased estimators, balanced incomplete blocks designs, inadmissibility, interblock information, confidence intervals
Brown, L. D., & Cohen, A. (1974). Point and Confidence Estimation of a Common Mean and Recovery of Interblock Information. The Annals of Statistics, 2 (5), 963-976. http://dx.doi.org/10.1214/aos/1176342817
Date Posted: 27 November 2017
This document has been peer reviewed.