Adaptive Inference for the Two-Sample Scale Problem

Abstract

Some adaptive tests are proposed (a) for the general two-sample scale problem and (b) for the restricted two-sample scale problem, in which the random variables are known to be right-skewed and also positive valued. These are based on either the ratio of the adaptively trimmed sample variances or adaptive rank tests of scale, whose quantiles are estimated by means of the bootstrap. Simulations show that, for practical sample sizes, these tests tend to perform better than their competitors. The methodology is illustrated by an application to a problem considered by Nair regarding the breakdown times of an insulating fluid under elevated voltage stress.

KEY WORDS:

• Bootstrap
• Monte Carlo studies
• Tests of homogeneity of variances