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Geometry of exponential family with competing risks and censored data

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  • 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
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    References listed on IDEAS

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    1. 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.
    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. 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.
    5. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
    6. 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.
    7. 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.
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    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.

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