IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i1p190-201.html
   My bibliography  Save this article

Nonparametric estimation in [alpha]-series processes

Author

Listed:
  • Aydogdu, Halil
  • Kara, Mahmut

Abstract

A counting process with the interoccurrence times X1,X2,... is an [alpha]-series process if there exists a real number [alpha] such that (k[alpha]Xk)k=1,2,... forms a renewal process. The nonparametric inference problem in an [alpha]-series process is taken into consideration. The Mann test is applied for trend analysis and a graphical technique is presented in order to test whether the data come from an [alpha]-series process. Some nonparametric estimators for three important parameters of the [alpha]-series process are obtained by using a linear regression method. The consistency and asymptotic normality properties are investigated. The performances of the estimators are evaluated by a simulation study. Some suggestions on the choice of the estimators are made based on the theoretical and simulation results. Further, the method is illustrated through a real-life example.

Suggested Citation

  • Aydogdu, Halil & Kara, Mahmut, 2012. "Nonparametric estimation in [alpha]-series processes," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 190-201, January.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:1:p:190-201
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311002544
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Lam Yeh & So Kuen Chan, 1998. "Statistical inference for geometric processes with lognormal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 27(1), pages 99-112, March.
    2. Chan, Jennifer S. K. & Lam, Yeh & Leung, Doris Y. P., 2004. "Statistical inference for geometric processes with gamma distributions," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 565-581, October.
    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. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).

    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. Chan, Jennifer So Kuen & Wan, Wai Yin, 2014. "Multivariate generalized Poisson geometric process model with scale mixtures of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 72-87.
    2. Chan, J.S.K. & Lam, C.P.Y. & Yu, P.L.H. & Choy, S.T.B. & Chen, C.W.S., 2012. "A Bayesian conditional autoregressive geometric process model for range data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3006-3019.
    3. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    4. Chen, Jianwei & Li, Kim-Hung & Lam, Yeh, 2010. "Bayesian computation for geometric process in maintenance problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 771-781.
    5. J.S.K. Chan & W.Y. Wan & P.L.H. Yu, 2014. "A Poisson geometric process approach for predicting drop-out and committed first-time blood donors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1486-1503, July.
    6. Jennifer Chan & Doris Leung, 2010. "Binary geometric process model for the modeling of longitudinal binary data with trend," Computational Statistics, Springer, vol. 25(3), pages 505-536, September.
    7. Tang, Ya-yong & Lam, Yeh, 2006. "A [delta]-shock maintenance model for a deteriorating system," European Journal of Operational Research, Elsevier, vol. 168(2), pages 541-556, January.
    8. Chan, Jennifer S. K. & Lam, Yeh & Leung, Doris Y. P., 2004. "Statistical inference for geometric processes with gamma distributions," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 565-581, October.
    9. Chen, Jinyuan & Li, Zehui, 2008. "An extended extreme shock maintenance model for a deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1123-1129.
    10. Wan, Wai-Yin & Chan, Jennifer So-Kuen, 2011. "Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 687-702, January.
    11. Lam, Yeh & Zhang, Yuan Lin & Liu, Qun, 2006. "A geometric process model for M/M/1 queueing system with a repairable service station," European Journal of Operational Research, Elsevier, vol. 168(1), pages 100-121, January.
    12. Lam, Yeh & Zhang, Yuan Lin & Zheng, Yao Hui, 2002. "A geometric process equivalent model for a multistate degenerative system," European Journal of Operational Research, Elsevier, vol. 142(1), pages 21-29, October.
    13. Lam, Yeh, 2007. "A geometric process maintenance model with preventive repair," European Journal of Operational Research, Elsevier, vol. 182(2), pages 806-819, October.

    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:56:y:2012:i:1:p:190-201. 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.