IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v446y2016icp234-245.html
   My bibliography  Save this article

Geometry of exponential family with competing risks and censored data

Author

Listed:
  • Zhang, Fode
  • Shi, Yimin

Abstract

Employing the differential geometrical methods in statistics suggested by Amari (1985) and Amari et al. (1987), considering the exponential family with censored data and competing risks as a manifold of a statistical model, the geometry of the manifold is investigated based on two information sources. As an application of the geometry, the asymptotic expansions of the bootstrap prediction, Bayesian prediction and their risk evaluations are investigated. The results show that these expansions are related to the coefficients of α-connections and metric tensors, and the predictive density function is the estimative density function in the asymptotic sense. Finally, taking Rayleigh distribution and prostatic cancer data as examples, some computation and simulation results are presented to illustrate our main results.

Suggested Citation

  • Zhang, Fode & Shi, Yimin, 2016. "Geometry of exponential family with competing risks and censored data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 234-245.
    • Handle: RePEc:eee:phsmap:v:446:y:2016:i:c:p:234-245
    DOI: 10.1016/j.physa.2015.12.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115010237
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2015.12.003?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. Tadayoshi Fushiki & Fumiyasu Komaki & Kazuyuki Aihara, 2004. "On Parametric Bootstrapping and Bayesian Prediction," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 403-416, September.
    2. Amari, Shun-ichi & Ohara, Atsumi & Matsuzoe, Hiroshi, 2012. "Geometry of deformed exponential families: Invariant, dually-flat and conformal geometries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4308-4319.
    3. Cramer, Erhard & Schmiedt, Anja Bettina, 2011. "Progressively Type-II censored competing risks data from Lomax distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1285-1303, March.
    4. Balakrishnan, N. & So, H.Y. & Ling, M.H., 2015. "EM algorithm for one-shot device testing with competing risks under exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 137(C), pages 129-140.
    5. Feizjavadian, S.H. & Hashemi, R., 2015. "Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 19-34.
    6. Erhard Cramer & Miriam Tamm, 2014. "On a Correction of the Scale MLE for a Two-Parameter Exponential Distribution Under Progressive Type-I Censoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(20), pages 4401-4414, October.
    7. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
    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. Fode Zhang & Hon Keung Tony Ng & Yimin Shi & Ruibing Wang, 2019. "Amari–Chentsov structure on the statistical manifold of models for accelerated life tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 77-105, March.
    2. Zhang, Fode & Shi, Yimin & Wang, Ruibing, 2017. "Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 552-565.
    3. Liu, Yiming & Shi, Yimin & Bai, Xuchao & Zhan, Pei, 2018. "Reliability estimation of a N-M-cold-standby redundancy system in a multicomponent stress–strength model with generalized half-logistic distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 231-249.
    4. Himanshu Rai & Sanjeev K. Tomer & Anoop Chaturvedi, 2021. "Robust estimation with variational Bayes in presence of competing risks," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 207-223, 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. Sun, Yanqing & Li, Mei & Gilbert, Peter B., 2016. "Goodness-of-fit test of the stratified mark-specific proportional hazards model with continuous mark," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 348-358.
    2. Zhang, Fode & Shi, Yimin & Wang, Ruibing, 2017. "Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 552-565.
    3. Subhankar Dutta & Suchandan Kayal, 2023. "Inference of a competing risks model with partially observed failure causes under improved adaptive type-II progressive censoring," Journal of Risk and Reliability, , vol. 237(4), pages 765-780, August.
    4. Rui Hua & Wenhao Gui, 2022. "Inference for copula-based dependent competing risks model with step-stress accelerated life test under generalized progressive hybrid censoring," Computational Statistics, Springer, vol. 37(5), pages 2399-2436, November.
    5. Manoj Chacko & Rakhi Mohan, 2019. "Bayesian analysis of Weibull distribution based on progressive type-II censored competing risks data with binomial removals," Computational Statistics, Springer, vol. 34(1), pages 233-252, March.
    6. Rui Hua & Wenhao Gui, 2022. "Revisit to progressively Type-II censored competing risks data from Lomax distributions," Journal of Risk and Reliability, , vol. 236(3), pages 377-394, June.
    7. Man-Ho Ling, 2022. "Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models," Mathematics, MDPI, vol. 10(5), pages 1-13, March.
    8. Refah Alotaibi & Ehab M. Almetwally & Qiuchen Hai & Hoda Rezk, 2022. "Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    9. Tian, Yuzhu & Zhu, Qianqian & Tian, Maozai, 2015. "Estimation for mixed exponential distributions under type-II progressively hybrid censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 85-96.
    10. Syed Ejaz Ahmed & Reza Arabi Belaghi & Abdulkadir Hussein & Alireza Safariyan, 2024. "New and Efficient Estimators of Reliability Characteristics for a Family of Lifetime Distributions under Progressive Censoring," Mathematics, MDPI, vol. 12(10), pages 1-18, May.
    11. López-Fidalgo, J. & Rivas-López, M.J., 2014. "Optimal experimental designs for partial likelihood information," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 859-867.
    12. Wang, Liang & Tripathi, Yogesh Mani & Dey, Sanku & Zhang, Chunfang & Wu, Ke, 2022. "Analysis of dependent left-truncated and right-censored competing risks data with partially observed failure causes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 285-307.
    13. Soumya Roy & Biswabrata Pradhan, 2023. "Inference for log‐location‐scale family of distributions under competing risks with progressive type‐I interval censored data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 208-232, May.
    14. Suparna Basu & Sanjay K. Singh & Umesh Singh, 2019. "Estimation of Inverse Lindley Distribution Using Product of Spacings Function for Hybrid Censored Data," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1377-1394, December.
    15. K. V. Harsha & Alladi Subramanyam, 2020. "Some information inequalities for statistical inference," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1237-1256, October.
    16. Feizjavadian, S.H. & Hashemi, R., 2015. "Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 19-34.
    17. Julian Górny & Erhard Cramer, 2018. "Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 173-210, February.
    18. Ruhul Ali Khan & Murari Mitra, 2021. "Estimation issues in the Exponential–Logarithmic model under hybrid censoring," Statistical Papers, Springer, vol. 62(1), pages 419-450, February.
    19. Wu, Shuo-Jye & Hsu, Chu-Chun & Huang, Syuan-Rong, 2020. "Optimal designs and reliability sampling plans for one-shot devices with cost considerations," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    20. Ping Chan & Hon Ng & Feng Su, 2015. "Exact likelihood inference for the two-parameter exponential distribution under Type-II progressively hybrid censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 747-770, August.

    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:phsmap:v:446:y:2016:i:c:p:234-245. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.