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Deficiency bounds for the multivariate inverse hypergeometric distribution.

Authors :
Ouimet, Frédéric
Source :
Statistical Papers; Aug2024, Vol. 65 Issue 6, p3959-3969, 11p
Publication Year :
2024

Abstract

The multivariate inverse hypergeometric (MIH) distribution is an extension of the negative multinomial (NM) model that accounts for sampling without replacement in a finite population. Even though most studies on longitudinal count data with a specific number of 'failures' occur in a finite setting, the NM model is typically chosen over the more accurate MIH model. This raises the question: How much information is lost when inferring with the approximate NM model instead of the true MIH model? The loss is quantified by a measure called deficiency in statistics. In this paper, asymptotic bounds for the deficiencies between MIH and NM experiments are derived, as well as between MIH and the corresponding multivariate normal experiments with the same mean-covariance structure. The findings are supported by a local approximation for the log-ratio of the MIH and NM probability mass functions, and by Hellinger distance bounds. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
09325026
Volume :
65
Issue :
6
Database :
Complementary Index
Journal :
Statistical Papers
Publication Type :
Academic Journal
Accession number :
178208743
Full Text :
https://doi.org/10.1007/s00362-023-01524-y