IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v74y2022i5d10.1007_s10463-022-00820-y.html
   My bibliography  Save this article

Adaptive efficient estimation for generalized semi-Markov big data models

Author

Listed:
  • Vlad Stefan Barbu

    (Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS-Université de Rouen Normandie)

  • Slim Beltaief

    (ALTEN de Toulouse)

  • Serguei Pergamenchtchikov

    (Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS-Université de Rouen Normandie
    Tomsk State University)

Abstract

In this paper we study generalized semi-Markov high dimension regression models in continuous time, observed at fixed discrete time moments. The generalized semi-Markov process has dependent jumps and, therefore, it is an extension of the semi-Markov regression introduced in Barbu et al. (Stat Inference Stoch Process 22:187–231, 2019a). For such models we consider estimation problems in nonparametric setting. To this end, we develop model selection procedures for which sharp non-asymptotic oracle inequalities for the robust risks are obtained. Moreover, we give constructive sufficient conditions which provide through the obtained oracle inequalities the adaptive robust efficiency property in the minimax sense. It should be noted also that, for these results, we do not use neither sparse conditions nor the parameter dimension in the model. As examples, regression models constructed through spherical symmetric noise impulses and truncated fractional Poisson processes are considered. Numerical Monte-Carlo simulations confirming the theoretical results are given in the supplementary materials.

Suggested Citation

  • Vlad Stefan Barbu & Slim Beltaief & Serguei Pergamenchtchikov, 2022. "Adaptive efficient estimation for generalized semi-Markov big data models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 925-955, October.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:5:d:10.1007_s10463-022-00820-y
    DOI: 10.1007/s10463-022-00820-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-022-00820-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-022-00820-y?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. Slim Beltaief & Oleg Chernoyarov & Serguei Pergamenchtchikov, 2020. "Model selection for the robust efficient signal processing observed with small Lévy noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1205-1235, October.
    2. Kou Fujimori, 2019. "The Dantzig selector for a linear model of diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 475-498, October.
    3. D. Fourdrinier & S. Pergamenshchikov, 2007. "Improved Model Selection Method for a Regression Function with Dependent Noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 435-464, September.
    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. Vlad Stefan Barbu & Guglielmo D’Amico & Andreas Makrides, 2022. "A Continuous-Time Semi-Markov System Governed by Stepwise Transitions," Mathematics, MDPI, vol. 10(15), pages 1-12, August.

    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. Slim Beltaief & Oleg Chernoyarov & Serguei Pergamenchtchikov, 2020. "Model selection for the robust efficient signal processing observed with small Lévy noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1205-1235, October.
    2. E. A. Pchelintsev & S. M. Pergamenshchikov, 2018. "Oracle inequalities for the stochastic differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 469-483, July.
    3. Evgeny Pchelintsev & Serguei Pergamenshchikov & Maria Povzun, 2022. "Efficient estimation methods for non-Gaussian regression models in continuous time," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 113-142, February.
    4. Evgeny Pchelintsev, 2013. "Improved estimation in a non-Gaussian parametric regression," Statistical Inference for Stochastic Processes, Springer, vol. 16(1), pages 15-28, April.
    5. Evgeny Pchelintsev & Serguei Pergamenshchikov & Maria Leshchinskaya, 2022. "Improved estimation method for high dimension semimartingale regression models based on discrete data," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 537-576, October.
    6. Victor Konev & Serguei Pergamenchtchikov, 2010. "General model selection estimation of a periodic regression with a Gaussian noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(6), pages 1083-1111, December.
    7. Victor, Konev & Serguei, Pergamenchtchikov, 2015. "Robust model selection for a semimartingale continuous time regression from discrete data," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 294-326.
    8. Kou Fujimori, 2022. "The variable selection by the Dantzig selector for Cox’s proportional hazards model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 515-537, June.
    9. L. Galtchouk & S. Pergamenshchikov, 2009. "Sharp non-asymptotic oracle inequalities for non-parametric heteroscedastic regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(1), pages 1-18.

    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:spr:aistmt:v:74:y:2022:i:5:d:10.1007_s10463-022-00820-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.