Exact Moments of Residuals of Independence

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

Mathematics, 2024, vol. 12, issue 24, 1-13

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.

Keywords: exact kurtosis; exact moments; exact skewness; residual of independence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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