MINIMAX ESTIMATION OF A VARIANCE

The nonparametric problem of estimating a variance based on a sample o f size n from a univariate distribution which has a known bounded rang e but is otherwise arbitrary is treated. For squared error loss, a cer tain linear function of the sample variance is seen to be minimax for each n from 2 through 13, except n = 4. For squared error loss weighte d by the reciprocal of the variance, a constant multiple of the sample variance is minimax for each n from 2 through 11. The least favorable distribution for these cases gives probability one to the Bernoulli d istributions.