SOME BOUNDS FOR BIAS AND VARIANCE OF S-2 UNDER DEPENDENCE

As is well known, the ordinary sample variance S-2 is an unbiased esti mator of the variance sigma(Z) when the observations X(1),...,X(n) eac h have a common expectation mu and a common variance sigma(2). In this article we derive bounds for the bias and variance of the S-2-statist ic when the X(i)-variables may be correlated and have unequal means an d variances. These bounds serve as a means for assessing the influence on S-2 when the standard assumptions do not hold. This is illustrated by some examples. In addition a limit theorem for S-2 is obtained.