Testing Joint Hypotheses When One of the Alternatives is One-Sided

45 Pages Posted: 15 Jan 2012

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

Walter Distaso

Imperial College Business School

Date Written: May 26, 2006

Abstract

We propose a class of statistics where the direction of one of the alternatives is incorporated. It is obtained by 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 one-sided inequality restrictions, and their distributions do not require bounds-based inference. We derive explicit distribution and power functions, using them to prove some desirable properties of our class of modified tests. We then illustrate the relevance of the method by applying it to devising an improved test of random walks in autoregressive models with deterministic components. In this example, the usual alternative to a unit root is one-sided in the direction of stable roots, while deterministic components are allowed to go either way, and we show that it is beneficial to take the partially one-sided nature of the alternative into account.

Suggested Citation

Abadir, Karim M. and Distaso, Walter, Testing Joint Hypotheses When One of the Alternatives is One-Sided (May 26, 2006). Available at SSRN: https://ssrn.com/abstract=1985282 or http://dx.doi.org/10.2139/ssrn.1985282

Karim M. Abadir (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/portal/page?_pageid=61,629646&_dad=portallive&_schema=PORTALLIVE

Walter Distaso

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

Register to save articles to
your library

Register

Paper statistics

Downloads
21
Abstract Views
261
PlumX Metrics