We study the limiting behavior of sums of functions of nearest neighbor distances for an $m$ dimensional sample. We establish a central limit theorem and moment bounds for such sums and an invariance principle for the empirical process of nearest neighbor distances. As a consequence we obtain the asymptotic behavior of a practicable goodness of fit test based on nearest neighbor distances.
Publié le : 1983-02-14
Classification:
Nearest neighbor distances,
goodness of fit,
asymptotics,
60F05,
62G10
@article{1176993668,
author = {Bickel, Peter J. and Breiman, Leo},
title = {Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit Test},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 185-214},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993668}
}
Bickel, Peter J.; Breiman, Leo. Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit Test. Ann. Probab., Tome 11 (1983) no. 4, pp. 185-214. http://gdmltest.u-ga.fr/item/1176993668/