A double decomposition of the test of independence of sets of variables that allows for a modeling view of this test

Carlos Manuel Agra Coelho; Filipe José Gonçalves Pereira Marques

A double decomposition of the test of independence of sets of variables that allows for a modeling view of this test

Carlos Manuel Agra Coelho, Filipe José Gonçalves Pereira Marques

DM - Departamento de Matemática

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In first place a decomposition of the l.r.t. (likelihood ratio test) statistic to test the independence between a set of variables and a given number of other sets of variables into a number of independent l.r.t. statistics is presented. This decomposition induces a decomposition of the null hypothesis for this test, which allows for a different view over the test. Then, based on this decomposition, a double decomposition of the l.r.t. statistic to test the independence of m sets of variables is presented which itself induces a double decomposition of the null hypothesis of independence among m sets of variables which in turn allows for a different view and interpretation of this test. These decompositions are much useful in helping us to relate these tests and interpret them under a modeling point of view.

Original language	Unknown
Title of host publication	Mathematics and Computers in Science and Engineering Series
Pages	13-19
Publication status	Published - 1 Jan 2014
Event	16th International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems - Duration: 1 Jan 2014 → …

Conference

Conference	16th International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems
Period	1/01/14 → …

Cite this

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title = "A double decomposition of the test of independence of sets of variables that allows for a modeling view of this test",

abstract = "In first place a decomposition of the l.r.t. (likelihood ratio test) statistic to test the independence between a set of variables and a given number of other sets of variables into a number of independent l.r.t. statistics is presented. This decomposition induces a decomposition of the null hypothesis for this test, which allows for a different view over the test. Then, based on this decomposition, a double decomposition of the l.r.t. statistic to test the independence of m sets of variables is presented which itself induces a double decomposition of the null hypothesis of independence among m sets of variables which in turn allows for a different view and interpretation of this test. These decompositions are much useful in helping us to relate these tests and interpret them under a modeling point of view.",

keywords = "near-exact distributions, likelihood ratio tests, multivariate linear models, exact distributions",

author = "Coelho, {Carlos Manuel Agra} and Marques, {Filipe Jos{\'e} Gon{\c c}alves Pereira}",

year = "2014",

month = jan,

day = "1",

language = "Unknown",

isbn = "978-960-474-396-4",

pages = "13--19",

booktitle = "Mathematics and Computers in Science and Engineering Series",

note = "16th International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems ; Conference date: 01-01-2014",

}

A double decomposition of the test of independence of sets of variables that allows for a modeling view of this test. / Coelho, Carlos Manuel Agra ; Marques, Filipe José Gonçalves Pereira.
Mathematics and Computers in Science and Engineering Series. 2014. p. 13-19.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A double decomposition of the test of independence of sets of variables that allows for a modeling view of this test

AU - Coelho, Carlos Manuel Agra

AU - Marques, Filipe José Gonçalves Pereira

PY - 2014/1/1

Y1 - 2014/1/1

N2 - In first place a decomposition of the l.r.t. (likelihood ratio test) statistic to test the independence between a set of variables and a given number of other sets of variables into a number of independent l.r.t. statistics is presented. This decomposition induces a decomposition of the null hypothesis for this test, which allows for a different view over the test. Then, based on this decomposition, a double decomposition of the l.r.t. statistic to test the independence of m sets of variables is presented which itself induces a double decomposition of the null hypothesis of independence among m sets of variables which in turn allows for a different view and interpretation of this test. These decompositions are much useful in helping us to relate these tests and interpret them under a modeling point of view.

AB - In first place a decomposition of the l.r.t. (likelihood ratio test) statistic to test the independence between a set of variables and a given number of other sets of variables into a number of independent l.r.t. statistics is presented. This decomposition induces a decomposition of the null hypothesis for this test, which allows for a different view over the test. Then, based on this decomposition, a double decomposition of the l.r.t. statistic to test the independence of m sets of variables is presented which itself induces a double decomposition of the null hypothesis of independence among m sets of variables which in turn allows for a different view and interpretation of this test. These decompositions are much useful in helping us to relate these tests and interpret them under a modeling point of view.

KW - near-exact distributions

KW - likelihood ratio tests

KW - multivariate linear models

KW - exact distributions

M3 - Conference contribution

SN - 978-960-474-396-4

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EP - 19

BT - Mathematics and Computers in Science and Engineering Series

T2 - 16th International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems

Y2 - 1 January 2014

ER -