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Large sample properties for a class of copulas in bivariate survival analysis

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Listed:
  • José Romeo
  • Nelson Tanaka
  • Antonio Pedroso-de-Lima
  • Victor Salinas-Torres

Abstract

This work is concerned with asymptotic properties of the bivariate survival function estimator using the functional relationship between marginal survival functions and a class of copulas for the dependence structure. Specifically, we study consistency and weak convergence of the bivariate survival function estimator obtained considering a two-step procedure of estimation. The obtained results are found from a key decomposition of the bivariate survival function in quantities that can be studied separately. In particular, we use relating results to almost sure and weak convergence of estimators, almost sure convergence of uniformly equicontinuous functions, and the delta method for functionals. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • José Romeo & Nelson Tanaka & Antonio Pedroso-de-Lima & Victor Salinas-Torres, 2013. "Large sample properties for a class of copulas in bivariate survival analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 997-1015, November.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:8:p:997-1015
    DOI: 10.1007/s00184-012-0428-2
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    References listed on IDEAS

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    1. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
    2. Klara Goethals & Paul Janssen & Luc Duchateau, 2008. "Frailty models and copulas: similarities and differences," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(9), pages 1071-1079.
    3. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
    4. Kouros Owzar & Pranab Kumar Sen, 2003. "Copulas: concepts and novel applications," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 323-353.
    5. Gerda Claeskens & Rosemary Nguti & Paul Janssen, 2008. "One-sided tests in shared frailty models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 69-82, May.
    6. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
    7. Yi Li & Ross L. Prentice & Xihong Lin, 2008. "Semiparametric maximum likelihood estimation in normal transformation models for bivariate survival data," Biometrika, Biometrika Trust, vol. 95(4), pages 947-960.
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