Abstract
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 minim ax-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.
Original language | English (US) |
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Pages (from-to) | 75-87 |
Number of pages | 13 |
Journal | Annals of Statistics |
Volume | 28 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2000 |
Keywords
- Adaptation with respect to estimation strategies
- Density estimation
- Minimax adaptation
- Rates of convergence