Brunk studied integral regression functions and has obtained strong laws and limiting distributions for estimators of these functions. In this note we will study additional conditions that ensure a rate of convergence of the distribution function of the maximum absolute difference of an integral regression function and its estimator, suitably normalized, to the distribution function of a normalized maximum absolute value of partial sums of random variables. These results are corollaries of convergence results obtained by Sawyer and Rosenkrantz.
Publié le : 1974-07-14
Classification:
Integral regression function,
maximum absolute value of partial sum,
independent observations regression model,
60F05,
62G05,
62G10,
60G50
@article{1176342772,
author = {Makowski, Gary},
title = {A Rate of Convergence of a Distribution Connected with Integral Regression Function Estimation},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 829-832},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342772}
}
Makowski, Gary. A Rate of Convergence of a Distribution Connected with Integral Regression Function Estimation. Ann. Statist., Tome 2 (1974) no. 1, pp. 829-832. http://gdmltest.u-ga.fr/item/1176342772/