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Asymptotic normality of the NPMLE of linear functionals for interval censored data, case 1

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  • J. Huang
  • J. A. Wellner

Abstract

We give a new proof of the asymptotic normality of a class of linear functionals of the nonparametric maximum likelihood estimator (NPMLE) of a distribution function with “case 1” interval censored data. In particular our proof simplifies the proof of asymptotic normality of the mean given in Groeneboom and Wellner (1992). The proof relies strongly on a rate of convergence result due to van de Geer (1993), and methods from empirical process theory.

Suggested Citation

  • J. Huang & J. A. Wellner, 1995. "Asymptotic normality of the NPMLE of linear functionals for interval censored data, case 1," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 49(2), pages 153-163, July.
    • Handle: RePEc:bla:stanee:v:49:y:1995:i:2:p:153-163
    DOI: 10.1111/j.1467-9574.1995.tb01462.x
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    Cited by:

    1. N. Balakrishnan & Xingqiu Zhao, 2011. "A class of multi-sample nonparametric tests for panel count data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 135-156, February.
    2. Yuan, Ao & Xu, Jinfeng & Zheng, Gang, 2012. "Root-n estimability of some missing data models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 147-166.
    3. Chun Yin Lee & Kin Yau Wong & Kwok Fai Lam & Dipankar Bandyopadhyay, 2023. "A semiparametric joint model for cluster size and subunit‐specific interval‐censored outcomes," Biometrics, The International Biometric Society, vol. 79(3), pages 2010-2022, September.
    4. Zhao, Xingqiu & Duan, Ran & Zhao, Qiang & Sun, Jianguo, 2013. "A new class of generalized log rank tests for interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 123-131.
    5. Toshio Honda, 2004. "Nonparametric regression with current status data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 49-72, March.
    6. Pao-sheng Shen & Yingwei Peng & Hsin-Jen Chen & Chyong-Mei Chen, 2022. "Maximum likelihood estimation for length-biased and interval-censored data with a nonsusceptible fraction," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 68-88, January.
    7. Andrews, Chris & van der Laan, Mark & Robins, James, 2005. "Locally efficient estimation of regression parameters using current status data," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 332-351, October.
    8. Ao Yuan & Anqi Yin & Ming T. Tan, 2021. "Enhanced Doubly Robust Procedure for Causal Inference," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(3), pages 454-478, December.

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