A trigamma-free approach for computing information matrices related to trigamma function

Zhou Yu (), Niloufar Dousti Mousavi () and Jie Yang ()
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Zhou Yu: University of Illinois at Chicago
Niloufar Dousti Mousavi: University of Chicago
Jie Yang: University of Illinois at Chicago

Statistical Papers, 2024, vol. 65, issue 7, No 7, 4179-4199

Abstract: Abstract Negative binomial related distributions have been widely used in practice. The calculation of the corresponding Fisher information matrices involves the expectation of trigamma function values which can only be calculated numerically and approximately. In this paper, we propose a trigamma-free approach to approximate the expectations involving the trigamma function, along with theoretical upper bounds for approximation errors. We show by numerical studies that our approach is highly efficient and much more accurate than previous methods. We also apply our approach to compute the Fisher information matrices of zero-inflated negative binomial (ZINB) and beta negative binomial (ZIBNB) probabilistic models, as well as ZIBNB regression models.

Keywords: Beta negative binomial distribution; Fisher information matrix; Negative binomial distribution; ZINB; ZIBNB (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-024-01552-2

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