Abstract.
For the invariant decision problem of estimating a continuous distribution function F with two entropy loss functions, it is proved that the best invariant estimators d 0 exist and are the same as the best invariant estimator of a continuous distribution function under the squared error loss function L (F, d)=∫|F (t) −d (t) |2 dF (t). They are minimax for any sample size n≥1.
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Mohammadi, L., van Zwet, W. Minimax invariant estimation of a continuous distribution function under entropy loss. Metrika 56, 31–42 (2002). https://doi.org/10.1007/s001840100152
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DOI: https://doi.org/10.1007/s001840100152