Abstract
In this paper, we first examine the sampling properties of the Graybill-Deal estimator when two normal population means may not be common. It is shown that the mean squared error of the Graybill-Deal estimator can be larger than that of the sample mean based on only one sample even if the difference between two population means are relatively small. From the result, we may conduct a pre-test for equality of two population means, and may use the Graybill-Deal estimator or the sample mean based on only one sample according to the result of the pre-test. We secondly examine the sampling properties of the pre-test estimator by Monte Carlo experiments. It is shown that the relatively large mean squared error of the Graybill-Deal estimator when the difference of two population means is relatively large can be substantially reduced by conducting thepre-test.
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