Journal
PROBABILITY THEORY AND RELATED FIELDS
Volume 159, Issue 3-4, Pages 479-543Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-013-0512-1
Keywords
Density estimation; Oracle inequality; Adaptive estimation; Kernel estimators; L-p-risk
Categories
Funding
- ISF [104/11]
Ask authors/readers for more resources
We address the problem of adaptive minimax density estimation on with -loss on the anisotropic Nikol'skii classes. We fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk. In particular, we show that there are four different regimes with respect to the behavior of the minimax risk. We develop a single estimator which is (nearly) optimal in order over the complete scale of the anisotropic Nikol'skii classes. Our estimation procedure is based on a data-driven selection of an estimator from a fixed family of kernel estimators.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available