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

Author

Listed:
  • Zhou Yu

    (University of Illinois at Chicago)

  • Niloufar Dousti Mousavi

    (University of Chicago)

  • Jie Yang

    (University of Illinois at Chicago)

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.

Suggested Citation

  • Zhou Yu & Niloufar Dousti Mousavi & Jie Yang, 2024. "A trigamma-free approach for computing information matrices related to trigamma function," Statistical Papers, Springer, vol. 65(7), pages 4179-4199, September.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:7:d:10.1007_s00362-024-01552-2
    DOI: 10.1007/s00362-024-01552-2
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    References listed on IDEAS

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    1. Fukang Zhu, 2011. "A negative binomial integer‐valued GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(1), pages 54-67, January.
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