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Kolmogorov–Smirnov 损失下最佳不变分布函数估计量的极小极大性AI 解读

For the invariant decision problem of estimating a continuous distribution function with the Kolmogorov-Smirnov loss, it is proved that the best invariant estimator is minimax.

Kolmogorov–Smirnov损失下分布函数的最优不变估计AI 解读

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…