COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 731

"The Exact Distribution of the Wald Statistic: The Non Central Case"

Peter C.B. Phillips and Sam Ouliaris

November 1984

This paper extends earlier results, which were reported in [7], to include non null distributions. As in [7], attention is concentrated on the Wald statistic for testing general linear restrictions on the coefficients in the multivariate linear model. The results of the present paper encompass the null distributions derived in [7] and generalize all previously known results for such statistics as the standard regression F test and Hotelling’s T ² test.

JEL Classification: 211

Keywords: Wald statistic, noncentral quadratic forms, distribution theory, matrix fractional calculus