The estimator proposed by Brunk for the indefinite integral of a regression function defined on the unit cube in $\beta$ dimensional Euclidean space is studied. It is shown to be strongly uniformly consistent if the errors satisfy a first moment type of condition and an almost sure rate of convergence of order $O((n/\log_2n)^{-1/2})$ is obtained.
Publié le : 1981-03-14
Classification:
Integral regression functions,
laws of the iterated logarithm,
partially ordered index sets,
60F15,
62E20
@article{1176345412,
author = {Wright, F. T.},
title = {Sums of Random Variables Indexed by a Partially Ordered Set and the Estimation of Integral Regression Functions},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 449-452},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345412}
}
Wright, F. T. Sums of Random Variables Indexed by a Partially Ordered Set and the Estimation of Integral Regression Functions. Ann. Statist., Tome 9 (1981) no. 1, pp. 449-452. http://gdmltest.u-ga.fr/item/1176345412/