TESTING JOINT HYPOTHESES WHEN ONE OF THE ALTERNATIVES IS ONE-SIDED

Karim ABADIR (University of York, UK)
Walter DISTASO (University of York, UK)

We propose a class of statistics where the direction of one of the alternatives is incorporated. It is founded on modifying a class of multivariate tests with elliptical confidence regions, not necessarily arising from Normal-based distribution theory. The resulting statistics are easy to compute, they do not require the re-estimation of models subject to inequality restrictions, and their distributions do not require bounds-based inference. We derive exact explicit distributions, then prove some desirable properties of our class of modified tests. We then illustrate the relevance of the method to practical problems by applying it to devising an improved test of random walks in autoregressive models with deterministic components.