Bounds for the variance of the graybill-deal estimator of the common mean of two normal distributions

Abstract

In this note we derive sharp lower and upper bounds for the variance of the Graybill-Deal estimator of the common mean of two normal distributions with unknown variances when the sample sizes are not necessarily equal. We also derive similar bounds for the variance of the Brown-Cohen (1974) T _a(1) class of unbiased es-timators to which the Graybill-Deal estimator belongs. Further, we illustrate the sharpness of the bounds by numerical computations in the case of the Graybill-Deal estimator.

Keywords:

• Brown-cohen estimator
• common mean of two normal distributions
• graybill-deal estimator
• sharp variance bounds