By Topic

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

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

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 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 )