Minimax invariant estimation of a continuous distribution function under entropy loss |
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| Authors: | Leila Mohammadi Willem R van Zwet |
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| Institution: | (1) Mathematical Institute, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands. (e-mails: leila@math.leidenuniv.nl, vanzwet@math.leidenuniv.nl), NL |
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| 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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| Keywords: | |
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