Asymptotically exact minimax estimation in sup-norm for anisotropic Hölder classes
By Karine Bertin. 2004
31 citations recorded by the source corpus.
Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Numerical Analysis
- Alexander Goldenshluger
- Anatoli B. Juditsky
- Alexandre B. Tsybakov
- O. Lepski
- I. Castillo
- Lin Xiao
- Tommaso Cai
- Jing Lei
In Statistics and Probability
- O. Lepski
- Alexander Goldenshluger
- Alexandre B. Tsybakov
- Anatoli B. Juditsky
- Yen-Chi Chen
- Shahar Mendelson
- Johannes Schmidt-Hieber
- Philippe Rigollet
Citations in the corpus
- Universal pointwise selection rule in multivariate function estimation (2008, background): “(2001) and Bertin (2004)) that for any α ∈Aγ , the minimax rate of convergence on Hd(α,L) is given by ε. Thus, FAH(γ,L) is the union of functional classes with prescribed accuracy of estimation. Klutchnikoff (2005) showed that the rate ε is not achievable on FAH(γ,L) and proved that the minimax rate”
- NONPARAMETRIC ESTIMATION OF COMPOSITE FUNCTIONS (2009, background): “It can be taken as a maximum of the last expression in square brackets over (γ,β) ∈ [1,2]2.”
- Structural adaptation via Lp-norm oracle inequalities (2007, background): “(3) [cf. Ibragimov and Khasminskii (1982), Stone (1982), Nussbaum (1987), Bertin (2004)].”