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Estimation with left-truncated and right censored data: A comparison study


  • Ahmadi, Jafar
  • Doostparast, Mahdi
  • Parsian, Ahmad


Estimation based on the left-truncated and right randomly censored data arising from a general family of distributions is considered. In the special case, when the random variables satisfy a proportional hazard model, the maximum likelihood estimators (MLEs) as well as the uniformly minimum variance unbiased estimators (UMVUEs) of the unknown parameters are obtained. Explicit expressions for the MLEs are obtained when the random variables follow an exponential distribution. In the latter case, three different estimators for the parameter of interest are proposed. These estimators are compared using the criteria of mean squared error (MSE) and Pitman measure of closeness (PMC). It is shown that shrinking does not always yield a better estimator.

Suggested Citation

  • Ahmadi, Jafar & Doostparast, Mahdi & Parsian, Ahmad, 2012. "Estimation with left-truncated and right censored data: A comparison study," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1391-1400.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1391-1400
    DOI: 10.1016/j.spl.2012.03.017

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    References listed on IDEAS

    1. Chiung-Yu Huang & Jing Qin, 2011. "Nonparametric estimation for length-biased and right-censored data," Biometrika, Biometrika Trust, vol. 98(1), pages 177-186.
    2. Hwang, Yi-Ting & Wang, Chun-chao, 2008. "A goodness of fit test for left-truncated and right-censored data," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2420-2425, October.
    3. Nandi, Swagata & Dewan, Isha, 2010. "An EM algorithm for estimating the parameters of bivariate Weibull distribution under random censoring," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1559-1569, June.
    4. Shen, Pao-sheng, 2009. "Hazards regression for length-biased and right-censored data," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 457-465, February.
    5. Xiaodong Luo & Wei Yann Tsai, 2009. "Nonparametric estimation for right-censored length-biased data: a pseudo-partial likelihood approach," Biometrika, Biometrika Trust, vol. 96(4), pages 873-886.
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