Mathematical Sciences: Estimation of a Distribution or Survival Function

研究生存函数和分布函数的统计非参数估计问题。对于存在右截尾数据的未知生存函数的损失函数范围，将得到极大极小估计。损失函数包括权重为Beta密度的Cramer-von Mises型损失函数。在一类类似的损失函数下，研究分布函数的最优不变估计的可容许性。对于Kolmogorov-Smirnov损失函数，我们将讨论相应的问题。

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.