## The Annals of Statistics

- Ann. Statist.
- Volume 2, Number 5 (1974), 963-976.

### Point and Confidence Estimation of a Common Mean and Recovery of Interblock Information

#### Abstract

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 $m \geqq 2$ and $n \geqq 3$. 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 $b \geqq 4$. 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.

#### Article information

**Source**

Ann. Statist., Volume 2, Number 5 (1974), 963-976.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176342817

**Digital Object Identifier**

doi:10.1214/aos/1176342817

**Mathematical Reviews number (MathSciNet)**

MR356334

**Zentralblatt MATH identifier**

0305.62019

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62F10: Point estimation

Secondary: 62K10: Block designs 62C15: Admissibility

**Keywords**

Common mean unbiased estimators balanced incomplete blocks designs inadmissibility interblock information confidence intervals

#### Citation

Brown, L. D.; Cohen, Arthur. Point and Confidence Estimation of a Common Mean and Recovery of Interblock Information. Ann. Statist. 2 (1974), no. 5, 963--976. doi:10.1214/aos/1176342817. https://projecteuclid.org/euclid.aos/1176342817