On adaptive minimax density estimation on $$R^d$$Rd
By Alexander Goldenshluger, O. Lepski. 2012
114 citations recorded by the source corpus.
We address the problem of adaptive minimax density estimation on $$\mathbb{R }^d$$Rd with $$\mathbb{L }_p$$Lp-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.
Subfields: Management Science and Operations Research, Numerical Analysis, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/1afb35f552aae266629e54f693a5a415d9cbfe99
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In Management Science and Operations Research
In Numerical Analysis
In Statistics and Probability
- I. Castillo
- Kolyan Ray
- Judith Rousseau
- Richard Nickl
- A. van der Vaart
- Subhashis Ghosal
- Botond Szab'o
- Stéphanie van der Pas
Citations in the corpus
- On Bayesian supremum norm contraction rates (2013, methodology): “We refer to Goldenshluger and Lepski [16] for an overview of current work in this area.”