Lifetime Data Analysis

, Volume 15, Issue 3, pp 295–315 | Cite as

About an adaptively weighted Kaplan-Meier estimate

  • Jean-François Plante


The minimum averaged mean squared error nonparametric adaptive weights use data from m possibly different populations to infer about one population of interest. The definition of these weights is based on the properties of the empirical distribution function. We use the Kaplan-Meier estimate to let the weights accommodate right-censored data and use them to define the weighted Kaplan-Meier estimate. The proposed estimate is smoother than the usual Kaplan-Meier estimate and converges uniformly in probability to the target distribution. Simulations show that the performances of the weighted Kaplan-Meier estimate on finite samples exceed that of the usual Kaplan-Meier estimate. A case study is also presented.


Adaptive weights Borrowing strength Kaplan-Meier estimate Nonparametrics Survival analysis Weighted inference 


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  1. Akaike H (1977) On entropy maximization principle. In: Krishnaiah PR (eds) Applications of statistics. North-Holland, Amsterdam, pp 27–41Google Scholar
  2. Breslow NE, Crowley J (1974) A large sample study of the life table and product limit estimates under random censorship. Ann Stat 2: 437–453MATHCrossRefMathSciNetGoogle Scholar
  3. Davison AC, Hinkley DV (1997) Bootstrap methods and their application. Cambridge University Press, New YorkMATHGoogle Scholar
  4. Efron B (1967) The two sample problem with censored data. Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, vol 4. University of California, Berkeley, pp 831–853Google Scholar
  5. Efron B (1981) Censored data and the bootstrap. J Am Stat Assoc 76: 312–319MATHCrossRefMathSciNetGoogle Scholar
  6. Földes A, Rejtö L (1981) Strong uniform consistency for nonparametric survival curve estimators from randomly censored data. Ann Stat 9: 122–129MATHCrossRefGoogle Scholar
  7. Hu F (1994) Relevance weighted smoothing and a new bootstrap method. Unpublished doctoral dissertation, Department of Statistics, The University of British Columbia, 177 ppGoogle Scholar
  8. Hu F, Zidek JV (1993) A relevance weighted nonparametric quantile estimator. Technical report no 134, Department of Statistics, The University of British Columbia, VancouverGoogle Scholar
  9. Hu F, Zidek JV (2002) The weighted likelihood. Can J Stat 30: 347–371MATHCrossRefMathSciNetGoogle Scholar
  10. Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53: 457–481MATHCrossRefMathSciNetGoogle Scholar
  11. Klein JP, Moeschberger ML (1997) Survival analysis: techniques for censored and truncated data. Springer-Verlag, New YorkMATHGoogle Scholar
  12. National Center for Health Statistics (1997) US decennial life tables for 1989–91, vol 1, no 1. Hyattsville, Maryland, 44 ppGoogle Scholar
  13. Plante JF (2007) Adaptive likelihood weights and mixtures of empirical distributions. Unpublished doctoral dissertation, Department of Statistics, The University of British Columbia, 171 ppGoogle Scholar
  14. Plante JF (2008) Nonparametric adaptive likelihood weights. Can J Stat 36: 443–461MATHMathSciNetCrossRefGoogle Scholar
  15. Plante JF (2009) On the asymptotic properties of the MAMSE adaptive likelihood weights. J Stat Plan Inference 139: 2147–2161MATHCrossRefMathSciNetGoogle Scholar
  16. Wang X (2001) Maximum weighted likelihood estimation. Unpublished doctoral dissertation, Department of Statistics, The University of British Columbia, 151 ppGoogle Scholar
  17. Wang X, van Eeden C, Zidek JV (2004) Asymptotic properties of maximum weighted likelihood estimators. J Stat Plan Inference 119: 37–54MATHCrossRefGoogle Scholar
  18. Wang X, Zidek JV (2005) Selecting likelihood weights by cross-validation. Ann Stat 33: 463–501MATHCrossRefMathSciNetGoogle Scholar
  19. Winter BB, Földes A, Rejtö L (1978) Glivenko-Cantelli theorems for the PL estimate. Prob Control Inf Theory 7: 213–225MATHGoogle Scholar

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Service d’enseignement des méthodes quantitatives de gestionHEC MontréalMontréalCanada

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