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Heterogeneous Overdispersed Count Data Regressions via Double-Penalized Estimations

Author

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  • Shaomin Li

    (Center for Statistics and Data Science, Beijing Normal University, Zhuhai 516087, China)

  • Haoyu Wei

    (Department of Statistics, North Carolina State University, Raleigh, NC 27695, USA)

  • Xiaoyu Lei

    (Department of Statistics, University of Chicago, Chicago, IL 60637, USA)

Abstract

Recently, the high-dimensional negative binomial regression (NBR) for count data has been widely used in many scientific fields. However, most studies assumed the dispersion parameter as a constant, which may not be satisfied in practice. This paper studies the variable selection and dispersion estimation for the heterogeneous NBR models, which model the dispersion parameter as a function. Specifically, we proposed a double regression and applied a double ℓ 1 -penalty to both regressions. Under the restricted eigenvalue conditions, we prove the oracle inequalities for the lasso estimators of two partial regression coefficients for the first time, using concentration inequalities of empirical processes. Furthermore, derived from the oracle inequalities, the consistency and convergence rate for the estimators are the theoretical guarantees for further statistical inference. Finally, both simulations and a real data analysis demonstrate that the new methods are effective.

Suggested Citation

  • Shaomin Li & Haoyu Wei & Xiaoyu Lei, 2022. "Heterogeneous Overdispersed Count Data Regressions via Double-Penalized Estimations," Mathematics, MDPI, vol. 10(10), pages 1-25, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1700-:d:816532
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    References listed on IDEAS

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    Cited by:

    1. Huiming Zhang & Haoyu Wei, 2022. "Sharper Sub-Weibull Concentrations," Mathematics, MDPI, vol. 10(13), pages 1-29, June.

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