Estimation of variance of sample variance in sample random sampling

Abstract

As it is known, the general m.v.u estimator of the variance of sample variance in simple random sampling is given by a linear combination with fixed coefficients of the fourth central moment and the square of the variance observed in the sample. In this paper, the best unbiased estimator is determined when the coefficient are allowed to depend on the moments of the standardized population. Explicit formulas are given for sapling with repetition. The results are illustrated on ten theoretical populations of different shape. By means of a simulation exercise it is investigated what happens when in the best estimator population moment, assumed unknown, are substituted by the corresponding sample moments. In the appendix other results concerning the fourth central moment and the square of variance are given.