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Risk estimation for nonparametric discrimination and estimation rules: A simulation study (Corresp.)

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2 Author(s)

The designer of a nonparametric discrimination or estimation procedure is almost always interested in the conditional risk of his procedure, or nde, conditioned on the available data. Unfortunately, L_{n} , the risk conditioned on a data set containing n observations, cannot be computed without exact knowledge of the underlying probability distribution functions. Since such knowledge is unavailable, the designer must be content with estimates of L_{n} . Two such estimates are the deleted estimate, L_{n}^{D} , and the holdout estimate, L_{n}^{H} . This paper presents the results of an experimental study of these two estimates and compares these results with some recently obtained distribution.free theoretical results. Among other things, the experimental data indicates that for k -nearest neighbor rules in {\bf R^{1}} with several examples of underlying distributions, P \{ \mid L_{n} - L^{D}_{n} \mid \geq \epsilon \} \geq 2e^{-2 \epsilon^{2}n} mbox{ P \{ \mid L_{n} - L^{H}_{n} \mid \geq \epsilon \} 2e^{-2 \epsilon^{2} \sqrt{n}} .}

Published in:

IEEE Transactions on Information Theory  (Volume:25 ,  Issue: 6 )