Efficiency of confidence intervals generated by repeated subsample calculations

Abstract

Confidence intervals for a mean may be obtained from n observations continuously and symmetrically distributed about the mean, by computing the means of all 2n − 1 subsets, or subsamples, of the observations. The true mean lies in each of the intervals between the ordered subsample means with probability 2−n. In order to reduce the 2n − 1 computations of means, a random subset of subsample means may be used, or a ‘ balanced’ subset may be selected satisfying certain group theoretic requirements. The full set, random subset and balanced subset method are evaluated by comparing the average lengths of corresponding confidence intervals when the observations are a sample from a normal distribution. For small numbers of observations, empirical sampling is used, and for large numbers asymptotic theory. The principal conclusion is that balanced subsets are significantly more efficient than random subsets for small numbers of subsample means, but that their superiority is small for large numbers of subsample means, say greater than 31, enough to make the more easily remembered and generated random subsets more favourable.