Geodesic
Some asymptotic properties between smooth empirical and quantile processes for dependent random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 565-580

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\widehat F_n$ be the smooth empirical estimator obtained by integrating a kernel type density estimator based on a random sample of size $n$ from continuous distribution function $F$. The almost sure deviation between smooth empirical and smooth quantile processes is investigated under $\phi$-mixing and strong mixing conditions. We derive a pointwise as well as a uniform Bahadur–Kieffer type representation for smooth quantiles under cases of $\phi$-mixing and strong mixing. These results extend those of Babu and Singh [J. Multivariate Anal., 8 (1978), pp. 532–549] and Ralescu [J. Statist. Plann. Inference, 32 (1992), pp. 243–258].
Keywords: kernel density estimator, almost sure deviation, smooth empirical process, smooth quantile process. 
@article{TVP_2021_66_3_a8,
     author = {S. Sun and W. Zhu},
     title = {Some asymptotic properties between smooth empirical and quantile processes for dependent random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {565--580},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a8/}
}
TY  - JOUR
AU  - S. Sun
AU  - W. Zhu
TI  - Some asymptotic properties between smooth empirical and quantile processes for dependent random variables
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2021
SP  - 565
EP  - 580
VL  - 66
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a8/
LA  - ru
ID  - TVP_2021_66_3_a8
ER  - 
%0 Journal Article
%A S. Sun
%A W. Zhu
%T Some asymptotic properties between smooth empirical and quantile processes for dependent random variables
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2021
%P 565-580
%V 66
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a8/
%G ru
%F TVP_2021_66_3_a8
S. Sun; W. Zhu. Some asymptotic properties between smooth empirical and quantile processes for dependent random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 565-580. http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a8/