You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Mixing Strategies for Density Estimation
The Annals of Statistics
Vol. 28, No. 1 (Feb., 2000), pp. 75-87
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2673982
Page Count: 13
You can always find the topics here!Topics: Estimators, Density estimation, Minimax, Density, Statistical estimation, Statism, Entropy, Consistent estimators, Sample size, Statistical models
Were these topics helpful?See something inaccurate? Let us know!
Select the topics that are inaccurate.
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
General results on adaptive density estimation are obtained with respect to any countable collection of estimation strategies under Kullback-Leibler and squared L2 losses. It is shown that without knowing which strategy works best for the underlying density, a single strategy can be constructed by mixing the proposed ones to be adaptive in terms of statistical risks. A consequence is that under some mild conditions, an asymptotically minimax-rate adaptive estimator exists for a given countable collection of density classes; that is, a single estimator can be constructed to be simultaneously minimax-rate optimal for all the function classes being considered. A demonstration is given for high-dimensional density estimation on [0, 1]d where the constructed estimator adapts to smoothness and interaction-order over some piecewise Besov classes and is consistent for all the densities with finite entropy.
The Annals of Statistics © 2000 Institute of Mathematical Statistics