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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

    ()

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    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

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    File URL: http://hdl.handle.net/10.1007/s11749-012-0281-7
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    Bibliographic Info

    Article provided by Springer in its journal TEST.

    Volume (Year): 21 (2012)
    Issue (Month): 4 (December)
    Pages: 790-810

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    Handle: RePEc:spr:testjl:v:21:y:2012:i:4:p:790-810

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    Related research

    Keywords: Generalized product-limit estimator; Convergence with rate; Almost sure representation; Asymptotic normality; Truncated and censored data; α-mixing; 62N02; 62G20;

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    References

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    1. Zhou, Yong, 1996. "A note on the TJW product-limit estimator for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 381-387, March.
    2. 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.
    3. Gijbels, I. & Wang, J. L., 1993. "Strong Representations of the Survival Function Estimator for Truncated and Censored Data with Applications," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 210-229, November.
    4. Gu, Minggao, 1995. "Convergence of increments for cumulative hazard function in a mixed censorship-truncation model with application to hazard estimators," Statistics & Probability Letters, Elsevier, vol. 23(2), pages 135-139, May.
    5. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
    6. Sun, Liuquan & Zhou, Yong, 1998. "Sequential confidence bands for densities under truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 31-41, September.
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    Cited by:
    1. Liang, Han-Ying & Liu, Ai-Ai, 2013. "Kernel estimation of conditional density with truncated, censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 40-58.

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