WEIGHTED ESTIMATORS FOR A NORMAL POPULATION VARIANCE

A weighted estimator for the variance of a normal distribution using a point guess value O(o)-2 (less-than-or-equal-to O-2) of the population variance O-2 is proposed. The weight considered is a function of the scalars a, b (0 less-than-or-equal-to a less-than-or-equal-to 1, b > 0) and the test statistic used for testing the hypothesis H(o): O-2 = O(o)-2. Keeping b fixed (a small number), three different estimates of a(min) (for which the mean square error of the weighted estimator is minimum) have been obtained and the corresponding estimators are proposed. The properties of the proposed estimators are studied and recommendations for their use are made.