The optimal estimator of the common variance of the different populations with known kurtosis

Searl and Intarapanich (1990) showed that when the kurtosis is known, the sample variance is dominated with respect to mean squared error by an improved estimator that makes use of that kurtosis for the single population. In this paper, we firstly show that the uniformly better unbiased estimator is dominated with respect to mean squared error by our new estimator that makes use of that kurtosis for two different population with the common variance. Next, expressions for the minimum mean squared error and the relative efficiency are given for the general distribution. The improvement, as measured by relative efficiency, is seen to be independent of the form of the distribution. Finally, we give some examples to explain that our new estimator is realizable. Moreover, the estimation procedure of the new estimator can also be extended to l (> 2) population by using the Cauchy-Schwarz inequality and Calculus.