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The strong law under a semiparametric model for truncated and censored data

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  • Sun, Liuquan

Abstract

In this paper we study integrals for any nonnegative measurable functions with respect to semiparametric estimators of the survival function and the cumulative hazard function based on left truncated and right censored data. The strong law of large numbers for these integrals is given. The results are useful in establishing strong consistency of many estimators under the semiparametric model for truncated and censored data.

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  • Sun, Liuquan, 2006. "The strong law under a semiparametric model for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1550-1558, August.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:14:p:1550-1558
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    References listed on IDEAS

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    1. 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.
    2. He, Shuyuan & Yang, Grace L., 2000. "On the strong convergence of the product-limit estimator and its integrals under censoring and random truncation," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 235-244, September.
    3. Sun, Liuquan & Zhu, Lixing, 2000. "A semiparametric model for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 217-227, July.
    4. 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.
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    Cited by:

    1. Subramanian, Sundarraman & Bandyopadhyay, Dipankar, 2008. "Semiparametric left truncation and right censorship models with missing censoring indicators," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2572-2577, November.
    2. Paulsen, Jostein & Lunde, Astrid & Skaug, Hans Julius, 2008. "Fitting mixed-effects models when data are left truncated," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 121-133, August.

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