IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v69y2014icp15-39.html
   My bibliography  Save this article

Statistical study of asymmetry in cell lineage data

Author

Listed:
  • de Saporta, Benoîte
  • Gégout-Petit, Anne
  • Marsalle, Laurence

Abstract

A rigorous methodology is proposed to study cell division data consisting in several observed genealogical trees of possibly different shapes. The procedure takes into account missing observations, data from different trees, as well as the dependence structure within genealogical trees. Its main new feature is the joint use of all available information from several data sets instead of single data set estimation, to avoid the drawbacks of low accuracy for estimators or low power for tests on small single trees. The data is modeled by an asymmetric bifurcating autoregressive process and possibly missing observations are taken into account by modeling the genealogies with a two-type Galton–Watson process. Least-squares estimators of the unknown parameters of the processes are given and symmetry tests are derived. Results are applied on real data of Escherichia coli division and an empirical study of the convergence rates of the estimators and power of the tests is conducted on simulated data.

Suggested Citation

  • de Saporta, Benoîte & Gégout-Petit, Anne & Marsalle, Laurence, 2014. "Statistical study of asymmetry in cell lineage data," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 15-39.
  • Handle: RePEc:eee:csdana:v:69:y:2014:i:c:p:15-39
    DOI: 10.1016/j.csda.2013.07.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313002703
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2013.07.025?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. de Saporta, Benoîte & Gégout-Petit, Anne & Marsalle, Laurence, 2012. "Asymmetry tests for bifurcating auto-regressive processes with missing data," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1439-1444.
    2. J. Zhou & I. V. Basawa, 2005. "Maximum Likelihood Estimation for a First‐Order Bifurcating Autoregressive Process with Exponential Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 825-842, November.
    3. Delmas, Jean-François & Marsalle, Laurence, 2010. "Detection of cellular aging in a Galton-Watson process," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2495-2519, December.
    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. Bernard Bercu & Vassili Blandin, 2015. "Limit theorems for bifurcating integer-valued autoregressive processes," Statistical Inference for Stochastic Processes, Springer, vol. 18(1), pages 33-67, April.
    2. Bercu, Bernard & Blandin, Vassili, 2015. "A Rademacher–Menchov approach for random coefficient bifurcating autoregressive processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1218-1243.
    3. Damien G Hicks & Terence P Speed & Mohammed Yassin & Sarah M Russell, 2019. "Maps of variability in cell lineage trees," PLOS Computational Biology, Public Library of Science, vol. 15(2), pages 1-32, February.
    4. S. Valère Bitseki Penda & Adélaïde Olivier, 2017. "Autoregressive functions estimation in nonlinear bifurcating autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 179-210, July.
    5. Vincent Bansaye & S. Valère Bitseki Penda, 2021. "A Phase Transition for Large Values of Bifurcating Autoregressive Models," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2081-2116, December.

    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. Bernard Bercu & Vassili Blandin, 2015. "Limit theorems for bifurcating integer-valued autoregressive processes," Statistical Inference for Stochastic Processes, Springer, vol. 18(1), pages 33-67, April.
    2. Vincent Bansaye & S. Valère Bitseki Penda, 2021. "A Phase Transition for Large Values of Bifurcating Autoregressive Models," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2081-2116, December.
    3. Bercu, Bernard & Blandin, Vassili, 2015. "A Rademacher–Menchov approach for random coefficient bifurcating autoregressive processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1218-1243.
    4. S. Valère Bitseki Penda & Adélaïde Olivier, 2017. "Autoregressive functions estimation in nonlinear bifurcating autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 179-210, July.
    5. Bitseki Penda, S. Valère, 2023. "Moderate deviation principles for kernel estimator of invariant density in bifurcating Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 282-314.
    6. Hoffmann, Marc & Marguet, Aline, 2019. "Statistical estimation in a randomly structured branching population," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5236-5277.
    7. Zhang, Chenhua, 2011. "Parameter estimation for first-order bifurcating autoregressive processes with Weibull innovations," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1961-1969.
    8. Vincent Bansaye, 2019. "Ancestral Lineages and Limit Theorems for Branching Markov Chains in Varying Environment," Journal of Theoretical Probability, Springer, vol. 32(1), pages 249-281, March.
    9. Hwang, S.Y. & Basawa, I.V., 2009. "Branching Markov processes and related asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1155-1167, July.
    10. Mao, Mingzhi, 2014. "The asymptotic behaviors for least square estimation of multi-casting autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 110-124.
    11. Hoffmann, Marc & Olivier, Adélaïde, 2016. "Nonparametric estimation of the division rate of an age dependent branching process," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1433-1471.
    12. Alsmeyer, Gerold & Gröttrup, Sören, 2016. "Branching within branching: A model for host–parasite co-evolution," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1839-1883.
    13. de Saporta, Benoîte & Gégout-Petit, Anne & Marsalle, Laurence, 2012. "Asymmetry tests for bifurcating auto-regressive processes with missing data," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1439-1444.
    14. S. Valère Bitseki Penda & Jean-François Delmas, 2023. "Central Limit Theorem for Kernel Estimator of Invariant Density in Bifurcating Markov Chains Models," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1591-1625, September.
    15. Terpstra, Jeff T. & Elbayoumi, Tamer, 2012. "A law of large numbers result for a bifurcating process with an infinite moving average representation," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 123-129.

    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:69:y:2014:i:c:p:15-39. 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.