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A necessary and sufficient condition for justifying non-parametric likelihood with censored data

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  • Qiqing Yu
  • Yuting Hsu
  • Kai Yu

Abstract

The non-parametric likelihood L(F) for censored data, including univariate or multivariate right-censored, doubly-censored, interval-censored, or masked competing risks data, is proposed by Peto (Appl Stat 22:86–91, 1973 ). It does not involve censoring distributions. In the literature, several noninformative conditions are proposed to justify L(F) so that the GMLE can be consistent (see, for examples, Self and Grossman in Biometrics 42:521–530 1986 , or Oller et al. in Can J Stat 32:315–326, 2004 ). We present the necessary and sufficient (N&S) condition so that $$L(F)$$ L ( F ) is equivalent to the full likelihood under the non-parametric set-up. The statement is false under the parametric set-up. Our condition is slightly different from the noninformative conditions in the literature. We present two applications to our cancer research data that satisfy the N&S condition but has dependent censoring. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Qiqing Yu & Yuting Hsu & Kai Yu, 2014. "A necessary and sufficient condition for justifying non-parametric likelihood with censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(8), pages 995-1011, November.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:8:p:995-1011
    DOI: 10.1007/s00184-014-0482-z
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    References listed on IDEAS

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    1. Qiqing Yu & G. Wong & Hao Qin & Jiaping Wang, 2012. "Random partition masking model for censored and masked competing risks data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 69-85, February.
    2. Yu, Qiqing & Qin, Hao & Wang, Jiaping, 2010. "About conditional masking probability models," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1174-1179, August.
    3. Anton Schick & Qiqing Yu, 2000. "Consistency of the GMLE with Mixed Case Interval‐Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 45-55, March.
    4. Qiqing Yu & George Wong & Linxiong Li, 2001. "Asymptotic Properties of Self-Consistent Estimators with Mixed Interval-Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 469-486, September.
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    Cited by:

    1. Marta García-Bárzana & Ana Belén Ramos-Guajardo & Ana Colubi & Erricos J. Kontoghiorghes, 2020. "Multiple linear regression models for random intervals: a set arithmetic approach," Computational Statistics, Springer, vol. 35(2), pages 755-773, June.

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    More about this item

    Keywords

    Right-censoring; Doubly-censoring; Masked competing risks data; Interval-censorship model; Multivariate censorship models; Primary 62 G05; Secondary 62 G20;
    All these keywords.

    JEL classification:

    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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