Discussiones Mathematicae Probability and Statistics 22(1,2) (2002) 37-51

EXACT DISTRIBUTION FOR THE GENERALIZED F TESTS

Miguel Fonseca, Joao Tiago Mexia

Department of Mathematics, Faculty of Science and Technology
New University of Lisbon
Monte da Caparica 2829-516 Caparica, Portugal
e-mail:
fonsecamig@yahoo.com

Roman Zmyślony

Institute of Mathematics, University of Zielona Góra
Podgórna 50 65-246 Zielona Góra, Poland
e-mail:
r.zmyslony@im.uz.zgora.pl

Abstract

Generalized F statistics are the quotients of convex combinations of central chi-squares divided by their degrees of freedom. Exact expressions are obtained for the distribution of these statistics when the degrees of freedom either in the numerator or in the denominator are even. An example is given to show how these expressions may be used to check the accuracy of Monte-Carlo methods in tabling these distributions. Moreover, when carrying out adaptative tests, these expressions enable us to estimate the p-values whenever they are available.

Keywords: exact distribution theory, hypothesis testing, generalized F distribution, adaptative test.

2000 Mathematics Subject Classification: 62E15, 62H10, 62H15, 62J10.

References

[1]
E. Gasiorek, A. Michalski and R. Zmyślony, Tests of independence of normal random variables with known and unknown variance ratio, Discussiones Mathematicae - Probability and Statistics 2 (2000), 237-247.
[2]
A.I. Khuri, T. Matthew and B.K. Sinha, Statistical Tests for Mixed Linear Models, John Wiley & Sons New York 1998.
[3]
A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310.
[4]
A. Michalski and R. Zmyślony, Testing hypothesis for linear functions of parameters in mixed linear models, Tatra Mt. Math. Pub. 17 (1999), 103-110.

Received 15 October 2002