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A simple estimator of the bivariate distribution function for censored gap times

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  • de Uña-Álvarez, Jacobo
  • Meira-Machado, Luis F.

Abstract

Let (T1,T2) be gap times corresponding to two consecutive events, which are observed subject to random right-censoring. In this paper a simple estimator of the bivariate distribution function of (T1,T2) is proposed. We investigate the conditions under which the introduced estimator is consistent. Applications to the estimation of the marginal distributions of the gap times and to correlation analysis are included. We explore the behaviour of the proposed methods through simulations.

Suggested Citation

  • de Uña-Álvarez, Jacobo & Meira-Machado, Luis F., 2008. "A simple estimator of the bivariate distribution function for censored gap times," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2440-2445, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2440-2445
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    References listed on IDEAS

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    1. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    2. Pena E.A. & Strawderman R.L. & Hollander M., 2001. "Nonparametric Estimation With Recurrent Event Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1299-1315, December.
    3. van der Laan M.J. & Hubbard A.E. & Robins J.M., 2002. "Locally Efficient Estimation of a Multivariate Survival Function in Longitudinal Studies," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 494-507, June.
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    1. repec:jss:jstsof:38:i03 is not listed on IDEAS
    2. Gustavo Soutinho & Luís Meira-Machado, 2023. "Nonparametric estimation of the distribution of gap times for recurrent events," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 103-128, March.
    3. Rotolo, Federico & Legrand, Catherine & Van Keilegom, Ingrid, 2011. "Simulation of clustered multi-state survival data based on a copula model," LIDAM Discussion Papers ISBA 2011040, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Amorim, Ana Paula & de Uña-Álvarez, Jacobo & Meira-Machado, Luís, 2011. "Presmoothing the transition probabilities in the illness-death model," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 797-806, July.

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