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Asymptotic properties of conditional distribution estimator with truncated, censored and dependent data

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  • Han-Ying Liang
  • Jacobo Uña-Álvarez
  • María Iglesias-Pérez

Abstract

In this paper we study the strong and weak convergence with rates for the estimators of the conditional distribution function as well as conditional cumulative hazard rate function for a left truncated and right censored model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. Also, the almost sure representations and asymptotic normality of the estimators are established. The finite sample performance of the estimators is investigated via simulations. Copyright Sociedad de Estadística e Investigación Operativa 2012

Suggested Citation

  • Han-Ying Liang & Jacobo Uña-Álvarez & María Iglesias-Pérez, 2012. "Asymptotic properties of conditional distribution estimator with truncated, censored and dependent data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 790-810, December.
    • Handle: RePEc:spr:testjl:v:21:y:2012:i:4:p:790-810
    DOI: 10.1007/s11749-012-0281-7
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    References listed on IDEAS

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    1. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
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    7. Jacobo de Uña-Álvarez & Han-Ying Liang & Alberto Rodríguez-Casal, 2010. "Nonlinear wavelet estimator of the regression function under left-truncated dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(3), pages 319-344.
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    Cited by:

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    2. Ana López-Cheda & Yingwei Peng & María Amalia Jácome, 2023. "Rejoinder on: Nonparametric estimation in mixture cure models with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 513-520, June.
    3. Yuanshan Wu & Guosheng Yin, 2017. "Multiple imputation for cure rate quantile regression with censored data," Biometrics, The International Biometric Society, vol. 73(1), pages 94-103, March.
    4. Han-Ying Liang & Jacobo Uña-álvarez & María Iglesias-pérez, 2015. "A Central Limit Theorem in Non-parametric Regression with Truncated, Censored and Dependent Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 256-269, March.
    5. Zohra Guessoum & Abdelkader Tatachak, 2020. "Asymptotic Results for Truncated-censored and Associated Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 142-164, May.
    6. Ana López-Cheda & Yingwei Peng & María Amalia Jácome, 2023. "Nonparametric estimation in mixture cure models with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 467-495, June.

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