Exact distribution for the generalized F tests

Miguel Fonseca; Joao Tiago Mexia; Roman Zmyślony

Discussiones Mathematicae Probability and Statistics (2002)

  • Volume: 22, Issue: 1-2, page 37-51
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Miguel Fonseca, Joao Tiago Mexia, and Roman Zmyślony. "Exact distribution for the generalized F tests." Discussiones Mathematicae Probability and Statistics 22.1-2 (2002): 37-51. <http://eudml.org/doc/287602>.

@article{MiguelFonseca2002,
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.},
author = {Miguel Fonseca, Joao Tiago Mexia, Roman Zmyślony},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {exact distribution theory; hypothesis testing; generalized F distribution; adaptative test; generalized distributions; adaptive tests},
language = {eng},
number = {1-2},
pages = {37-51},
title = {Exact distribution for the generalized F tests},
url = {http://eudml.org/doc/287602},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Miguel Fonseca
AU - Joao Tiago Mexia
AU - Roman Zmyślony
TI - Exact distribution for the generalized F tests
JO - Discussiones Mathematicae Probability and Statistics
PY - 2002
VL - 22
IS - 1-2
SP - 37
EP - 51
AB - 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.
LA - eng
KW - exact distribution theory; hypothesis testing; generalized F distribution; adaptative test; generalized distributions; adaptive tests
UR - http://eudml.org/doc/287602
ER -

References

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  1. [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. Zbl1123.62309
  2. [2] A.I. Khuri, T. Matthew and B.K. Sinha, Statistical Tests for Mixed Linear Models, John Wiley & Sons New York 1998. 
  3. [3] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310. Zbl0842.62059
  4. [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. Zbl0987.62012

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