Asymptotic Tests of Composite Hypotheses

Brown University Economics Working Paper No. 03-09

30 Pages Posted: 22 May 2003

See all articles by Peter Reinhard Hansen

Peter Reinhard Hansen

University of North Carolina (UNC) at Chapel Hill - Department of Economics; Copenhagen Business School, Finance; Aarhus University - CREATES

Date Written: April 2003


Test statistics that are suitable for testing composite hypotheses are typically non-pivotal, and conservative bounds are commonly used to test composite hypotheses. In this paper, we propose a testing procedure for composite hypotheses that incorporates additional sample information. This avoids, as n->oo, the use of conservative bounds and leads to tests with better power than standard tests. The testing procedure satisfies a novel similarity condition that is relevant for asymptotic tests of composite hypotheses, and we show that this is a necessary condition for a test to be unbiased. The procedure is particularly useful for simultaneous testing of multiple inequalities, in particular when the number of inequalities is large.This is the situation for the multiple comparisons of forecasting models, and we show that the new testing procedure dominates the 'reality check' of White (2000) and avoids certain pitfalls.

Keywords: Composite hypothesis, similar test, unbiased test, multiple comparisons

JEL Classification: C12, C30, C52, C53

Suggested Citation

Hansen, Peter Reinhard, Asymptotic Tests of Composite Hypotheses (April 2003). Brown University Economics Working Paper No. 03-09. Available at SSRN: or

Peter Reinhard Hansen (Contact Author)

University of North Carolina (UNC) at Chapel Hill - Department of Economics ( email )

Chapel Hill, NC 27599
United States

HOME PAGE: http://

Copenhagen Business School, Finance ( email )

Solbjerg Plads 3
Frederiksberg C, DK - 2000

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C

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