Data-Driven k-Sample Tests

Abstract

A new solution of the general nonparametric k-sample problem for independent continuous random variables is developed. Our approach to solving the nonparametric problem is via introducing a net of semiparametric models, solving the testing problem for members of this approximating net, and then combining the resulting statistics via model selection rules which mimic the rule proposed recently in Inglot and Ledwina (2006). We call such a solution a data-driven test. Since we in fact use a class of model selection criteria, we also obtain a class of k-sample data-driven tests. The class is flexible and allows us to construct omnibus as well as more specialized solutions. Simulations show that the new omnibus test has power comparable to existing k-sample tests in case of changes of location or scale, and is more powerful for much more complex changes. A variant of the new solution focused on detecting high-frequency alternations is also briefly discussed. Some theoretical support is given. This article is accompanied by supplemental materials available online at the Technometrics website.