IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i2p431-454.html
   My bibliography  Save this article

Estimation of two ordered bivariate mean residual life functions

Author

Listed:
  • Rojo, Javier
  • Ghebremichael, Musie

Abstract

Situations occur frequently in which the mean residual life (mrl) functions of two populations must be ordered. For example, if a mechanical device is improved, the mrl function for the improved device should not be less than that of the original device. Also, mrl functions for medical patients should often be ordered depending on the status of concomitant variables. This paper proposes nonparametric estimators of the bivariate mrl function under a mrl ordering. The estimators are shown to be asymptotically unbiased, strongly uniformly consistent and weakly convergent to a bivariate Gaussian process. The estimators are shown to be the projections, in a sense to be made precise, of the empirical mrl function onto an appropriate convex set of mrl functions. In the one-sample problem, the new estimators dominate the empirical mrl function in terms of risk with respect to a wide class of loss functions.

Suggested Citation

  • Rojo, Javier & Ghebremichael, Musie, 2006. "Estimation of two ordered bivariate mean residual life functions," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 431-454, February.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:431-454
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(05)00039-4
    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. Arnold, Barry C. & Zahedi, Hassan, 1988. "On multivariate mean remaining life functions," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 1-9, April.
    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. M. Shafaei Noughabi & M. Kayid, 2019. "Bivariate quantile residual life: a characterization theorem and statistical properties," Statistical Papers, Springer, vol. 60(6), pages 2001-2012, December.
    2. Yang, Guangren & Zhou, Yong, 2014. "Semiparametric varying-coefficient study of mean residual life models," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 226-238.

    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. Paduthol Gaduthol Sankaran & Bovas Abraham & Ansa Alphonsa Antony, 2006. "A dependence measure for bivariate failure time data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 327-341.
    2. Hu, Taizhong & Khaledi, Baha-Eldin & Shaked, Moshe, 2003. "Multivariate hazard rate orders," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 173-189, January.
    3. Paduthol Godan Sankaran & Narayanan Unnikrishnan Nair, 2004. "Partial moments for bivariate distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 339-351.
    4. S. Ashrafi & M. Asadi, 2015. "On the stochastic and dependence properties of the three-state systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 261-281, April.
    5. V. N. Sreeja & P. G. Sankaran, 2007. "Proportional mean residual life model for gap time distributions of recurrent events," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 319-336.
    6. Kumar Gupta, Sanjib & De, Soumen & Chatterjee, Aditya, 2017. "Some reliability issues for incomplete two-dimensional warranty claims data," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 64-77.

    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:jmvana:v:97:y:2006:i:2:p:431-454. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.