Mathematical Sciences: Estimation of a Distribution or Survival Function

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Research will be conducted on statistical nonparametric estimation problems about survival functions and distribution functions. Minimax estimators will be obtained for a range of loss functions for an unknown survival function in the presence of right-censored data. The loss functions include Cramer-von Mises type loss functions whose weights are Beta densities. The admissibility of the best invariant estimator of a distribution function will be examined under a similar class of loss functions. Corresponding questions will be examined for the case of Kolmogorov-Smirnov loss functions.