Exact Moments of Residuals of Independence
The diagnosis of residuals of independence is critical in association analysis and loglinear modeling of two-way contingency tables. Most residual diagnostics depend on large-sample methods, and diagnostic results become dubious when sample sizes are small or data are sparse. In such cases, statisti...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/24/3987 |
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| author | Xianggui Qu |
| author_facet | Xianggui Qu |
| author_sort | Xianggui Qu |
| collection | DOAJ |
| description | The diagnosis of residuals of independence is critical in association analysis and loglinear modeling of two-way contingency tables. Most residual diagnostics depend on large-sample methods, and diagnostic results become dubious when sample sizes are small or data are sparse. In such cases, statistical inference based on non-asymptotic theory or exact inference is desirable. This paper explicitly derives the first four moments of the residuals of independence in a two-way contingency table under a multinomial model. These exact moments are necessary tools for studying the analytical features of the distribution of residuals of independence, such as skewness and kurtosis. Higher-order moments can be found similarly, but the results are more complicated. |
| format | Article |
| id | doaj-art-d102a738626a4f7fafc2963ba42e19ed |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-d102a738626a4f7fafc2963ba42e19ed2025-08-20T02:43:49ZengMDPI AGMathematics2227-73902024-12-011224398710.3390/math12243987Exact Moments of Residuals of IndependenceXianggui Qu0Department of Mathematics and Statistics, Oakland University, 146 Library Drive, Rochester, MI 48309, USAThe diagnosis of residuals of independence is critical in association analysis and loglinear modeling of two-way contingency tables. Most residual diagnostics depend on large-sample methods, and diagnostic results become dubious when sample sizes are small or data are sparse. In such cases, statistical inference based on non-asymptotic theory or exact inference is desirable. This paper explicitly derives the first four moments of the residuals of independence in a two-way contingency table under a multinomial model. These exact moments are necessary tools for studying the analytical features of the distribution of residuals of independence, such as skewness and kurtosis. Higher-order moments can be found similarly, but the results are more complicated.https://www.mdpi.com/2227-7390/12/24/3987exact kurtosisexact momentsexact skewnessresidual of independence |
| spellingShingle | Xianggui Qu Exact Moments of Residuals of Independence Mathematics exact kurtosis exact moments exact skewness residual of independence |
| title | Exact Moments of Residuals of Independence |
| title_full | Exact Moments of Residuals of Independence |
| title_fullStr | Exact Moments of Residuals of Independence |
| title_full_unstemmed | Exact Moments of Residuals of Independence |
| title_short | Exact Moments of Residuals of Independence |
| title_sort | exact moments of residuals of independence |
| topic | exact kurtosis exact moments exact skewness residual of independence |
| url | https://www.mdpi.com/2227-7390/12/24/3987 |
| work_keys_str_mv | AT xiangguiqu exactmomentsofresidualsofindependence |