Spatially adaptive density estimation by localised Haar projections

@article{Gach2013,
abstract = {Given a random sample from some unknown density $f_\{0\}:\mathbb \{R\}\rightarrow [0,\infty )$ we devise Haar wavelet estimators for $f_\{0\}$ with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen and Spokoiny (Ann. Statist.25(1997) 927–947)). We show that these estimators satisfy an oracle inequality that adapts to heterogeneous smoothness of $f_\{0\}$, simultaneously for every point $x$ in a fixed interval, in sup-norm loss. The thresholding constants involved in the test procedures can be chosen in practice under the idealised assumption that the true density is locally constant in a neighborhood of the point $x$ of estimation, and an information theoretic justification of this practise is given.},
author = {Gach, Florian, Nickl, Richard, Spokoiny, Vladimir},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {spatial adaptation; propagation condition},
language = {eng},
number = {3},
pages = {900-914},
publisher = {Gauthier-Villars},
title = {Spatially adaptive density estimation by localised Haar projections},
url = {http://eudml.org/doc/271960},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Gach, Florian
AU - Nickl, Richard
AU - Spokoiny, Vladimir
TI - Spatially adaptive density estimation by localised Haar projections
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2013
PB - Gauthier-Villars
VL - 49
IS - 3
SP - 900
EP - 914
AB - Given a random sample from some unknown density $f_{0}:\mathbb {R}\rightarrow [0,\infty )$ we devise Haar wavelet estimators for $f_{0}$ with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen and Spokoiny (Ann. Statist.25(1997) 927–947)). We show that these estimators satisfy an oracle inequality that adapts to heterogeneous smoothness of $f_{0}$, simultaneously for every point $x$ in a fixed interval, in sup-norm loss. The thresholding constants involved in the test procedures can be chosen in practice under the idealised assumption that the true density is locally constant in a neighborhood of the point $x$ of estimation, and an information theoretic justification of this practise is given.
LA - eng
KW - spatial adaptation; propagation condition
UR - http://eudml.org/doc/271960
ER -