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A note on the TJW product-limit estimator for truncated and censored data

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  • Zhou, Yong

Abstract

Some almost sure representations are obtained for the TJW product-limit estimator of a distribution function when the data are subject to random left-truncation and right-censorship. These results extend the theorems of Stute (1993) which were obtained for purely truncated data.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:26:y:1996:i:4:p:381-387
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    References listed on IDEAS

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    1. Burke, Murray D. & Gombay, Edit, 1988. "On goodness-of-fit and the bootstrap," Statistics & Probability Letters, Elsevier, vol. 6(5), pages 287-293, April.
    2. Wellner, Jon A., 1981. "A Glivenko-Cantelli theorem for empirical measures of independent but non-identically distributed random variables," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 309-312, August.
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    Citations

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    Cited by:

    1. 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.
    2. Zhou, Yong & Yip, Paul S. F., 1999. "A Strong Representation of the Product-Limit Estimator for Left Truncated and Right Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 261-280, May.
    3. Iglesias-Pérez, M. C., 2003. "Strong representation of a conditional quantile function estimator with truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 65(2), pages 79-91, November.
    4. BuHamra, Sana S. & Al-Kandari, N.M.Noriah M. & Ahmed, S. E., 2004. "Inference concerning quantile for left truncated and right censored data," Computational Statistics & Data Analysis, Elsevier, vol. 46(4), pages 819-831, July.
    5. Sun, Liuquan & Zhu, Lixing, 2000. "A semiparametric model for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 217-227, July.
    6. Shi, Jianhua & Chen, Xiaoping & Zhou, Yong, 2015. "The strong representation for the nonparametric estimator of length-biased and right-censored data," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 49-57.
    7. 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.
    8. Jacobo Uña-álvarez, 2004. "Nonparametric estimation under length-biased sampling and Type I censoring: A moment based approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(4), pages 667-681, December.
    9. Zhao, Mu & Bai, Fangfang & Zhou, Yong, 2011. "Relative deficiency of quantile estimators for left truncated and right censored data," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1725-1732, November.
    10. Jacobo Uña-Álvarez, 2002. "Product-limit estimation for length-biased censored data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 109-125, June.
    11. Liang, Han-Ying & de Uña-Álvarez, Jacobo, 2011. "Wavelet estimation of conditional density with truncated, censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 448-467, March.

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