Best Invariant Estimation of a Distribution Function under the Kolmogorov-Smirnov Loss Function
Kolmogorov–Smirnov损失下分布函数的最优不变估计
Given a random sample of size $n$ from an unknown continuous distribution function $F$, we consider the problem of estimating $F$ nonparametrically from a decision theoretic approach. In our treatment, we assume the Kolmogorov-Smirnov loss function and the group of all one-to-one monotone transformations of real numbers onto themselves which leave the sample values invariant. Under this setup, we obtain a best invariant estimator of $F$ which is shown to be unique. This…