A Note on an Estimator for the Variance That Utilizes the Kurtosis

An estimator (S W 2) for the variance is developed by minimizing the mean squared error (MSE) using a generalized weight for the sum of squares instead of 1/(n . 1).The optimal divisor found is (n + 1) + (.4 . 3) (n 1 1)/n, where .4 is the kurtosis.For the normal distribution (.4 = 3), the divisor becomes n + 1.Generally, for kurtosis greater than 3 the divisor will be greater than n + 1 and for kurtosis less than 3 the divisor will be less than n + 1.Using n + 1 as a divisor will result in a smaller MSE for distributions with .4 > 3.