Geodesic
Complete convergence theorems for normed row sums from an array of rowwise pairwise negative quadrant dependent random variables with application to the dependent bootstrap
Applications of Mathematics, Tome 60 (2015) no. 3, pp. 251-263.

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

Let $\{X_{n,j}, 1\leq j\leq m(n), n\geq 1\}$ be an array of rowwise pairwise negative quadrant dependent mean 0 random variables and let $0$. Conditions are given for $\sum \nolimits _{j=1}^{m(n)}X_{n,j}/b_n\rightarrow 0$ completely and for $\max \nolimits _{1\leq k\leq m(n)}\Bigl |\sum \nolimits _{j=1}^kX_{n,j}\Big |/b_n\rightarrow 0$ completely. As an application of these results, we obtain a complete convergence theorem for the row sums $\sum \nolimits _{j=1}^{m(n)}X_{n,j}^*$ of the dependent bootstrap samples $\{\{X_{n,j}^*, 1\leq j\leq m(n)\}, n\geq 1\}$ arising from a sequence of i.i.d.\ random variables $\{X_n, n\geq 1\}$.
DOI : 10.1007/s10492-015-0094-6
Classification : 60F15, 62F40, 62G09
Keywords: array of rowwise pairwise negative quadrant dependent random variables; complete convergence; dependent bootstrap; sequence of i.i.d.\ random variables 
@article{10_1007_s10492_015_0094_6,
     author = {Rosalsky, Andrew and Wu, Yongfeng},
     title = {Complete convergence theorems for normed row sums from an array of rowwise pairwise negative quadrant dependent random variables with application to the dependent bootstrap},
     journal = {Applications of Mathematics},
     pages = {251--263},
     publisher = {mathdoc},
     volume = {60},
     number = {3},
     year = {2015},
     doi = {10.1007/s10492-015-0094-6},
     mrnumber = {3419961},
     zbl = {06486910},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0094-6/}
}
TY  - JOUR
AU  - Rosalsky, Andrew
AU  - Wu, Yongfeng
TI  - Complete convergence theorems for normed row sums from an array of rowwise pairwise negative quadrant dependent random variables with application to the dependent bootstrap
JO  - Applications of Mathematics
PY  - 2015
SP  - 251
EP  - 263
VL  - 60
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0094-6/
DO  - 10.1007/s10492-015-0094-6
LA  - en
ID  - 10_1007_s10492_015_0094_6
ER  - 
%0 Journal Article
%A Rosalsky, Andrew
%A Wu, Yongfeng
%T Complete convergence theorems for normed row sums from an array of rowwise pairwise negative quadrant dependent random variables with application to the dependent bootstrap
%J Applications of Mathematics
%D 2015
%P 251-263
%V 60
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0094-6/
%R 10.1007/s10492-015-0094-6
%G en
%F 10_1007_s10492_015_0094_6
Rosalsky, Andrew; Wu, Yongfeng. Complete convergence theorems for normed row sums from an array of rowwise pairwise negative quadrant dependent random variables with application to the dependent bootstrap. Applications of Mathematics, Tome 60 (2015) no. 3, pp. 251-263. doi : 10.1007/s10492-015-0094-6. http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0094-6/

Cité par Sources :