Abstract
For the invariant decision problem of estimating a continuous distribution function with the Kolmogorov-Smirnov loss within the class of ‘proper– distribution functions, it is proved that the sample distribution function is the best invariant estimator only for the sample size n = 1 and 2. Further it is shown that the best invariant estimator is minimax. Exact jumps of the best invariant estimator are derived for n ≤ 4.
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Chen, Z., Phadia, E. A Note on the Best Invariant Estimator of a Distribution Function Under the Kolmogorov-Smirnov Loss. Annals of the Institute of Statistical Mathematics 49, 231–235 (1997). https://doi.org/10.1023/A:1003154627756
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DOI: https://doi.org/10.1023/A:1003154627756