This paper provides an empirical central limit theorem (CLT) for exchangeable random variables when the norming constants in the regular CLT are with h(n) a slowly varying function. The situation with norming constants of the form nh(n) is also discussed.

Many statistical problems can be reformulated in terms of tests of uniformity. Some strong laws of large numbers and a central limit theorem for the logarithm of transformed spacings are obtained. These theorems provide a characterization of the uniform distribution. A general information-type...

Statistical evidence of a significant difference between the performance of a protected group and the majority on a preemployment exam is often critical when a court decides whether the exam has a disparate impact, that is, whether the exam has a disproportionate adverse impact on minority...