Measure of Departure from Point Symmetry and Decomposition of Measure for Square Contingency Tables
For square contingency tables with ordered categories, Tomizawa, Biometrica J. 28 (1986), 387–393, considered the conditional point symmetry model. Kurakami et al., J. Stat. Adv. Theory Appl. 17 (2017), 33–42, considered the another point symmetry and the reverse global symmetry model. The present p...
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| Format: | Article |
| Language: | English |
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Springer
2021-01-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
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| Online Access: | https://www.atlantis-press.com/article/125950415/view |
| _version_ | 1828410779568701440 |
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| author | Kiyotaka Iki Sadao Tomizawa |
| author_facet | Kiyotaka Iki Sadao Tomizawa |
| author_sort | Kiyotaka Iki |
| collection | DOAJ |
| description | For square contingency tables with ordered categories, Tomizawa, Biometrica J. 28 (1986), 387–393, considered the conditional point symmetry model. Kurakami et al., J. Stat. Adv. Theory Appl. 17 (2017), 33–42, considered the another point symmetry and the reverse global symmetry model. The present paper proposes Kullback–Leibler information type measures to represent the degree of departure from each of the models. Also this paper shows a theorem that the measure for the another point symmetry model is equal to the sum of the measures for the reverse global symmetry model and for the conditional point symmetry model. |
| first_indexed | 2024-12-10T12:17:01Z |
| format | Article |
| id | doaj.art-109fb3e82f5948c2b743d81e9a26d1f7 |
| institution | Directory Open Access Journal |
| issn | 2214-1766 |
| language | English |
| last_indexed | 2024-12-10T12:17:01Z |
| publishDate | 2021-01-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-109fb3e82f5948c2b743d81e9a26d1f72022-12-22T01:49:11ZengSpringerJournal of Statistical Theory and Applications (JSTA)2214-17662021-01-0119410.2991/jsta.d.201223.001Measure of Departure from Point Symmetry and Decomposition of Measure for Square Contingency TablesKiyotaka IkiSadao TomizawaFor square contingency tables with ordered categories, Tomizawa, Biometrica J. 28 (1986), 387–393, considered the conditional point symmetry model. Kurakami et al., J. Stat. Adv. Theory Appl. 17 (2017), 33–42, considered the another point symmetry and the reverse global symmetry model. The present paper proposes Kullback–Leibler information type measures to represent the degree of departure from each of the models. Also this paper shows a theorem that the measure for the another point symmetry model is equal to the sum of the measures for the reverse global symmetry model and for the conditional point symmetry model.https://www.atlantis-press.com/article/125950415/viewConditional symmetryGlobal symmetryKullback–Leibler informationMeasurePoint symmetrySquare contingency table |
| spellingShingle | Kiyotaka Iki Sadao Tomizawa Measure of Departure from Point Symmetry and Decomposition of Measure for Square Contingency Tables Journal of Statistical Theory and Applications (JSTA) Conditional symmetry Global symmetry Kullback–Leibler information Measure Point symmetry Square contingency table |
| title | Measure of Departure from Point Symmetry and Decomposition of Measure for Square Contingency Tables |
| title_full | Measure of Departure from Point Symmetry and Decomposition of Measure for Square Contingency Tables |
| title_fullStr | Measure of Departure from Point Symmetry and Decomposition of Measure for Square Contingency Tables |
| title_full_unstemmed | Measure of Departure from Point Symmetry and Decomposition of Measure for Square Contingency Tables |
| title_short | Measure of Departure from Point Symmetry and Decomposition of Measure for Square Contingency Tables |
| title_sort | measure of departure from point symmetry and decomposition of measure for square contingency tables |
| topic | Conditional symmetry Global symmetry Kullback–Leibler information Measure Point symmetry Square contingency table |
| url | https://www.atlantis-press.com/article/125950415/view |
| work_keys_str_mv | AT kiyotakaiki measureofdeparturefrompointsymmetryanddecompositionofmeasureforsquarecontingencytables AT sadaotomizawa measureofdeparturefrompointsymmetryanddecompositionofmeasureforsquarecontingencytables |