Maximum correlations and tests of goodness-of-fit

Hoeffding's maximum correlation coefficient equals unity when both distributions coincide. This fact suggests a method to test whether the cdf of an iid sequence of random variables is a given F, by computing this coefficient between F and the empirical cdf of the sequence. In this paper we present three instances of actual goodness-of-fit tests derived from this basic principle and we discuss their small- and large-sample properties.