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Heterogeneous Overdispersed Count Data Regressions via Double Penalized Estimations

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  • Shaomin Li
  • Haoyu Wei
  • Xiaoyu Lei

Abstract

This paper studies the non-asymptotic merits of the double $\ell_1$-regularized for heterogeneous overdispersed count data via negative binomial regressions. Under the restricted eigenvalue conditions, we prove the oracle inequalities for 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.

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  • Shaomin Li & Haoyu Wei & Xiaoyu Lei, 2021. "Heterogeneous Overdispersed Count Data Regressions via Double Penalized Estimations," Papers 2110.03552, arXiv.org, revised Feb 2022.
    • Handle: RePEc:arx:papers:2110.03552
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    References listed on IDEAS

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    1. Shengqi Tian & Dehui Wang & Shuai Cui, 2020. "A seasonal geometric INAR process based on negative binomial thinning operator," Statistical Papers, Springer, vol. 61(6), pages 2561-2581, December.
    2. Rafael Weißbach & Lucas Radloff, 2020. "Consistency for the negative binomial regression with fixed covariate," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 627-641, July.
    3. Shi, Chengchun & Song, Rui & Chen, Zhao & Li, Runze, 2019. "Linear hypothesis testing for high dimensional generalized linear models," LSE Research Online Documents on Economics 102108, London School of Economics and Political Science, LSE Library.
    4. Andreas Million & Regina T. Riphahn & Achim Wambach, 2003. "Incentive effects in the demand for health care: a bivariate panel count data estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 387-405.
    5. Dai, Hongsheng & Bao, Yanchun & Bao, Mingtang, 2013. "Maximum likelihood estimate for the dispersion parameter of the negative binomial distribution," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 21-27.
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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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