Abstract
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.
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References
Akaike H (1977) On entropy maximization principle. In: Krishnaiah PR (eds) Applications of statistics. North-Holland, Amsterdam, pp 27–41
Breslow NE, Crowley J (1974) A large sample study of the life table and product limit estimates under random censorship. Ann Stat 2: 437–453
Davison AC, Hinkley DV (1997) Bootstrap methods and their application. Cambridge University Press, New York
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 831–853
Efron B (1981) Censored data and the bootstrap. J Am Stat Assoc 76: 312–319
Földes A, Rejtö L (1981) Strong uniform consistency for nonparametric survival curve estimators from randomly censored data. Ann Stat 9: 122–129
Hu F (1994) Relevance weighted smoothing and a new bootstrap method. Unpublished doctoral dissertation, Department of Statistics, The University of British Columbia, 177 pp
Hu F, Zidek JV (1993) A relevance weighted nonparametric quantile estimator. Technical report no 134, Department of Statistics, The University of British Columbia, Vancouver
Hu F, Zidek JV (2002) The weighted likelihood. Can J Stat 30: 347–371
Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53: 457–481
Klein JP, Moeschberger ML (1997) Survival analysis: techniques for censored and truncated data. Springer-Verlag, New York
National Center for Health Statistics (1997) US decennial life tables for 1989–91, vol 1, no 1. Hyattsville, Maryland, 44 pp
Plante JF (2007) Adaptive likelihood weights and mixtures of empirical distributions. Unpublished doctoral dissertation, Department of Statistics, The University of British Columbia, 171 pp
Plante JF (2008) Nonparametric adaptive likelihood weights. Can J Stat 36: 443–461
Plante JF (2009) On the asymptotic properties of the MAMSE adaptive likelihood weights. J Stat Plan Inference 139: 2147–2161
Wang X (2001) Maximum weighted likelihood estimation. Unpublished doctoral dissertation, Department of Statistics, The University of British Columbia, 151 pp
Wang X, van Eeden C, Zidek JV (2004) Asymptotic properties of maximum weighted likelihood estimators. J Stat Plan Inference 119: 37–54
Wang X, Zidek JV (2005) Selecting likelihood weights by cross-validation. Ann Stat 33: 463–501
Winter BB, Földes A, Rejtö L (1978) Glivenko-Cantelli theorems for the PL estimate. Prob Control Inf Theory 7: 213–225
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Plante, JF. About an adaptively weighted Kaplan-Meier estimate. Lifetime Data Anal 15, 295–315 (2009). https://doi.org/10.1007/s10985-009-9120-x
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DOI: https://doi.org/10.1007/s10985-009-9120-x