IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2110.03552.html
   My bibliography  Save this paper

Heterogeneous Overdispersed Count Data Regressions via Double Penalized Estimations

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2110.03552
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Tansel, Aysit & Keskin, Halil Ibrahim, 2017. "Education Effects on Days Hospitalized and Days out of Work by Gender: Evidence from Turkey," IZA Discussion Papers 11210, Institute of Labor Economics (IZA).
    3. Greene, William, 2007. "Functional Form and Heterogeneity in Models for Count Data," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(2), pages 113-218, August.
    4. Erik Schokkaert & Tom Van Ourti & Diana De Graeve & Ann Lecluyse & Carine Van de Voorde, 2010. "Supplemental health insurance and equality of access in Belgium," Health Economics, John Wiley & Sons, Ltd., vol. 19(4), pages 377-395, April.
    5. Schmitz, Hendrik, 2013. "Practice budgets and the patient mix of physicians – The effect of a remuneration system reform on health care utilisation," Journal of Health Economics, Elsevier, vol. 32(6), pages 1240-1249.
    6. Sebastian Panthöfer, 2016. "Risk Selection under Public Health Insurance with Opt‐Out," Health Economics, John Wiley & Sons, Ltd., vol. 25(9), pages 1163-1181, September.
    7. Guo, Xu & Li, Runze & Liu, Jingyuan & Zeng, Mudong, 2023. "Statistical inference for linear mediation models with high-dimensional mediators and application to studying stock reaction to COVID-19 pandemic," Journal of Econometrics, Elsevier, vol. 235(1), pages 166-179.
    8. Caner, Mehmet, 2023. "Generalized linear models with structured sparsity estimators," Journal of Econometrics, Elsevier, vol. 236(2).
    9. Schmitz, Hendrik, 2008. "Do Optional Deductibles Reduce the Number of Doctor Visits? – Empirical Evidence with German Data," Ruhr Economic Papers 76, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    10. William Greene & Colin McKenzie, 2012. "LM Tests for Random Effects," Working Papers 12-14, New York University, Leonard N. Stern School of Business, Department of Economics.
    11. Y. Machnes, 2006. "The demand for private health care under national health insurance," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 7(4), pages 265-269, December.
    12. Massimiliano Bratti & Alfonso Miranda, 2010. "Endogenous Treatment Effects for Count Data Models with Sample Selection or Endogenous Participation," DoQSS Working Papers 10-05, Quantitative Social Science - UCL Social Research Institute, University College London, revised 10 Dec 2010.
    13. Daniel S. J. Lechmann & Claus Schnabel, 2014. "Absence from Work of the Self-Employed: A Comparison with Paid Employees," Kyklos, Wiley Blackwell, vol. 67(3), pages 368-390, August.
    14. Xiaojing Dong & Pradeep Chintagunta & Puneet Manchanda, 2011. "A new multivariate count data model to study multi-category physician prescription behavior," Quantitative Marketing and Economics (QME), Springer, vol. 9(3), pages 301-337, September.
    15. Vijverberg, Chu-Ping C. & Vijverberg, Wim P., 2012. "Pregibit: A Family of Discrete Choice Models," IZA Discussion Papers 6359, Institute of Labor Economics (IZA).
    16. Hossein Kavand & Marcel Voia, 2018. "Estimation of Health Care Demand and its Implication on Income Effects of Individuals," Springer Proceedings in Business and Economics, in: William H. Greene & Lynda Khalaf & Paul Makdissi & Robin C. Sickles & Michael Veall & Marcel-Cristia (ed.), Productivity and Inequality, pages 275-304, Springer.
    17. Bago d'Uva, Teresa & Jones, Andrew M. & van Doorslaer, Eddy, 2009. "Measurement of horizontal inequity in health care utilisation using European panel data," Journal of Health Economics, Elsevier, vol. 28(2), pages 280-289, March.
    18. Rodica Gilles & Seik Kim, 2013. "Distribution-Free Estimation of Zero-Inflated Models with Unobserved Heterogeneity," Working Papers UWEC-2013-03, University of Washington, Department of Economics.
    19. Greene, William, 2010. "Testing hypotheses about interaction terms in nonlinear models," Economics Letters, Elsevier, vol. 107(2), pages 291-296, May.
    20. William Greene, 2007. "Discrete Choice Modeling," Working Papers 07-6, New York University, Leonard N. Stern School of Business, Department of Economics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2110.03552. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.