Year: 2024
Type: article
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.
Source: Mathematics
DOI: 10.3390/math12243987
Author: Xianggui Qu
Institution: Oakland University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4405528085