Geodesic
Empirical estimator of the regularity index of a probability measure
Kybernetika, Tome 48 (2012) no. 4, pp. 589-599.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The index of regularity of a measure was introduced by Beirlant, Berlinet and Biau [1] to solve practical problems in nearest neighbour density estimation such as removing bias or selecting the number of neighbours. These authors proved the weak consistency of an estimator based on the nearest neighbour density estimator. In this paper, we study an empirical version of the regularity index and give sufficient conditions for its weak and strong convergence without assuming absolute continuity or other global properties of the underlying measure.
Classification : 62G05
Keywords: regularity index; Lebesgue point; small ball probability 
@article{KYB_2012__48_4_a1,
     author = {Berlinet, Alain and Servien, R\'emi},
     title = {Empirical estimator of the regularity index of a probability measure},
     journal = {Kybernetika},
     pages = {589--599},
     publisher = {mathdoc},
     volume = {48},
     number = {4},
     year = {2012},
     mrnumber = {3013392},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_4_a1/}
}
TY  - JOUR
AU  - Berlinet, Alain
AU  - Servien, Rémi
TI  - Empirical estimator of the regularity index of a probability measure
JO  - Kybernetika
PY  - 2012
SP  - 589
EP  - 599
VL  - 48
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2012__48_4_a1/
LA  - en
ID  - KYB_2012__48_4_a1
ER  - 
%0 Journal Article
%A Berlinet, Alain
%A Servien, Rémi
%T Empirical estimator of the regularity index of a probability measure
%J Kybernetika
%D 2012
%P 589-599
%V 48
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2012__48_4_a1/
%G en
%F KYB_2012__48_4_a1
Berlinet, Alain; Servien, Rémi. Empirical estimator of the regularity index of a probability measure. Kybernetika, Tome 48 (2012) no. 4, pp. 589-599. http://geodesic.mathdoc.fr/item/KYB_2012__48_4_a1/