COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 722

"The Exact Distribution of the Wald Statistic"

Peter C. B. Phillips

September 1984

This paper derives the exact distribution of the Wald statistic for testing general linear restrictions on the coefficients in the multivariate linear model. This generalizes all previously known results including those for the standard F statistic in linear regression, for Hotelling’s T ² test and for Hotelling's generalized T₀² test. Conventional classical assumptions of normally distributed errors and nonrandom exogenous variables are employed.

JEL Classification: 211

Keywords: Matrix fractional calculus, Wald statistic, distribution theory

See CFP 654