IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v93y2016icp209-227.html
   My bibliography  Save this article

Maximum likelihood estimation and expectation–maximization algorithm for controlled branching processes

Author

Listed:
  • González, M.
  • Minuesa, C.
  • del Puerto, I.

Abstract

The controlled branching process is a generalization of the classical Bienaymé–Galton–Watson branching process. It is a useful model for describing the evolution of populations in which the population size at each generation needs to be controlled. The maximum likelihood estimation of the parameters of interest for this process is addressed under various sample schemes. Firstly, assuming that the entire family tree can be observed, the corresponding estimators are obtained and their asymptotic properties investigated. Secondly, since in practice it is not usual to observe such a sample, the maximum likelihood estimation is initially considered using the sample given by the total number of individuals and progenitors of each generation, and then using the sample given by only the generation sizes. Expectation–maximization algorithms are developed to address these problems as incomplete data estimation problems. The accuracy of the procedures is illustrated by means of a simulated example.

Suggested Citation

  • González, M. & Minuesa, C. & del Puerto, I., 2016. "Maximum likelihood estimation and expectation–maximization algorithm for controlled branching processes," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 209-227.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:209-227
    DOI: 10.1016/j.csda.2015.01.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947315000262
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2015.01.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Miguel González & Rodrigo Martínez & Inés Puerto, 2004. "Nonparametric estimation of the offspring distribution and the mean for a controlled branching process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 465-479, December.
    2. Miguel González & Inés M. Puerto, 2012. "Diffusion Approximation of an Array of Controlled Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 843-861, September.
    3. Sriram, T.N. & Bhattacharya, A. & González, M. & Martínez, R. & del Puerto, I., 2007. "Estimation of the offspring mean in a controlled branching process with a random control function," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 928-946, July.
    4. Hautphenne, Sophie & Fackrell, Mark, 2014. "An EM algorithm for the model fitting of Markovian binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 19-34.
    5. Wang, Naichen & Wang, Lianming & McMahan, Christopher S., 2015. "Regression analysis of bivariate current status data under the Gamma-frailty proportional hazards model using the EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 140-150.
    6. Bercu, B., 1999. "Weighted estimation and tracking for Bienaymé Galton Watson processes with adaptive control," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 415-421, May.
    7. Bernhardt, Paul W. & Zhang, Daowen & Wang, Huixia Judy, 2015. "A fast EM algorithm for fitting joint models of a binary response and multiple longitudinal covariates subject to detection limits," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 37-53.
    8. Veen, Alejandro & Schoenberg, Frederic P., 2008. "Estimation of SpaceTime Branching Process Models in Seismology Using an EMType Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 614-624, June.
    9. Miguel González & Rodrigo Martínez & Iné Puerto, 2005. "Estimation of the variance for a controlled branching process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 199-213, June.
    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. Ramtirthkar, Mukund & Kale, Mohan, 2022. "A note on the local asymptotic mixed normality of a controlled branching process with a random control function," Statistics & Probability Letters, Elsevier, vol. 181(C).
    2. Nina Daskalova, 2017. "Expectation maximization estimates of the offspring probabilities in a class of multitype branching processes with binary family trees," Mathematical Population Studies, Taylor & Francis Journals, vol. 24(4), pages 246-256, October.

    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. Arpita Inamdar & Mohan Kale, 2016. "Joint Estimation of Offspring Mean and Offspring Variance of Controlled Branching Process," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 248-268, August.
    2. Sriram, T.N. & Bhattacharya, A. & González, M. & Martínez, R. & del Puerto, I., 2007. "Estimation of the offspring mean in a controlled branching process with a random control function," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 928-946, July.
    3. Xu, Yang & Zhao, Shishun & Hu, Tao & Sun, Jianguo, 2021. "Variable selection for generalized odds rate mixture cure models with interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    4. Maire, Florian & Moulines, Eric & Lefebvre, Sidonie, 2017. "Online EM for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 27-47.
    5. Zhang, Zili & Charalambous, Christiana & Foster, Peter, 2023. "A Gaussian copula joint model for longitudinal and time-to-event data with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    6. Mohler, George, 2014. "Marked point process hotspot maps for homicide and gun crime prediction in Chicago," International Journal of Forecasting, Elsevier, vol. 30(3), pages 491-497.
    7. Chiang, Wen-Hao & Liu, Xueying & Mohler, George, 2022. "Hawkes process modeling of COVID-19 with mobility leading indicators and spatial covariates," International Journal of Forecasting, Elsevier, vol. 38(2), pages 505-520.
    8. Peter Halpin & Paul Boeck, 2013. "Modelling Dyadic Interaction with Hawkes Processes," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 793-814, October.
    9. Chenlong Li & Zhanjie Song & Wenjun Wang, 2020. "Space–time inhomogeneous background intensity estimators for semi-parametric space–time self-exciting point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 945-967, August.
    10. Hautphenne, Sophie & Fackrell, Mark, 2014. "An EM algorithm for the model fitting of Markovian binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 19-34.
    11. Julio A. Crego, 2017. "Short Selling Ban and Intraday Dynamics," Working Papers wp2018_1715, CEMFI.
    12. Miguel González & Inés M. Puerto, 2012. "Diffusion Approximation of an Array of Controlled Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 843-861, September.
    13. Eric W. Fox & Martin B. Short & Frederic P. Schoenberg & Kathryn D. Coronges & Andrea L. Bertozzi, 2016. "Modeling E-mail Networks and Inferring Leadership Using Self-Exciting Point Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 564-584, April.
    14. Wheatley, Spencer & Filimonov, Vladimir & Sornette, Didier, 2016. "The Hawkes process with renewal immigration & its estimation with an EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 120-135.
    15. Giada Adelfio & Arianna Agosto & Marcello Chiodi & Paolo Giudici, 2021. "Financial contagion through space-time point processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 665-688, June.
    16. Angelos Dassios & Hongbiao Zhao, 2017. "A Generalized Contagion Process With An Application To Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-33, February.
    17. Donglin Zeng & Fei Gao & D. Y. Lin, 2017. "Maximum likelihood estimation for semiparametric regression models with multivariate interval-censored data," Biometrika, Biometrika Trust, vol. 104(3), pages 505-525.
    18. V. Filimonov & D. Sornette, 2015. "Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1293-1314, August.
    19. Murray, James & Philipson, Pete, 2022. "A fast approximate EM algorithm for joint models of survival and multivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    20. Murray, James & Philipson, Pete, 2023. "Fast estimation for generalised multivariate joint models using an approximate EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).

    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:eee:csdana:v:93:y:2016:i:c:p:209-227. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.