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Exact Moments of Residuals of Independence

Author

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  • Xianggui Qu

    (Department of Mathematics and Statistics, Oakland University, 146 Library Drive, Rochester, MI 48309, USA)

Abstract

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.

Suggested Citation

  • Xianggui Qu, 2024. "Exact Moments of Residuals of Independence," Mathematics, MDPI, vol. 12(24), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3987-:d:1547036
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