A Note on Vector-Valued Goodness-of-Fit Tests

Abstract

Vector-valued goodness-of-fit tests based on a single sample with possibly dependent components are considered. Sometimes, e.g., when combining both correlated and uncorrelated nonparametric or parametric tests of approximately the same power, vector-valued tests can provide a gain in power. Several examples of such a gain are presented.

Keywords:

• Power of goodness-of-fit tests
• Vector-valued tests

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62G10

Acknowledgment

The authors are grateful to Christos Skiadas who suggested submitting this paper to Communications in Statistics, to a referee for useful comments, and to Rosa Alloyarova for producing Monte Carlo simulations.