Independence in contingency tables using simplicial geometry

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F15%3A33155227" target="_blank" >RIV/61989592:15310/15:33155227 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1080/03610926.2013.824980" target="_blank" >http://dx.doi.org/10.1080/03610926.2013.824980</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/03610926.2013.824980" target="_blank" >10.1080/03610926.2013.824980</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Independence in contingency tables using simplicial geometry

Popis výsledku v původním jazyce

Frequently, contingency tables are generated in a multinomial sampling. Multinomial probabilities are then organized in a table assigning probabilities to each cell. A probability table can be viewed as an element in the simplex. The Aitchison geometry of the simplex identifies independent probability tables as a linear subspace. An important consequence is that, given a probability table, the nearest independent table is obtained by orthogonal projection onto the independent subspace. The nearest independent table is identified as that obtained by the product of geometric marginals, which do not coincide with the standard marginals, except in the independent case. The original probability table is decomposed into orthogonal tables, the independent andthe interaction tables. The underlying model is log-linear, and a procedure to test independence of a contingency table, based on a multinomial simulation, is developed. Its performance is studied on an illustrative example.

Název v anglickém jazyce

Independence in contingency tables using simplicial geometry

Popis výsledku anglicky

Frequently, contingency tables are generated in a multinomial sampling. Multinomial probabilities are then organized in a table assigning probabilities to each cell. A probability table can be viewed as an element in the simplex. The Aitchison geometry of the simplex identifies independent probability tables as a linear subspace. An important consequence is that, given a probability table, the nearest independent table is obtained by orthogonal projection onto the independent subspace. The nearest independent table is identified as that obtained by the product of geometric marginals, which do not coincide with the standard marginals, except in the independent case. The original probability table is decomposed into orthogonal tables, the independent andthe interaction tables. The underlying model is log-linear, and a procedure to test independence of a contingency table, based on a multinomial simulation, is developed. Its performance is studied on an illustrative example.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Communications in Statistics - Theory and Methods

ISSN

0361-0926

e-ISSN

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Svazek periodika

44

Číslo periodika v rámci svazku

18

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

3978-3996

Kód UT WoS článku

000362340800014

EID výsledku v databázi Scopus

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