| 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 (English) |
| Author:
|
Rosalsky, Andrew |
| Author:
|
Wu, Yongfeng |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
251-263 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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<b_n\rightarrow \infty $. 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 $\{X_n, n\geq 1\}$. (English) |
| Keyword:
|
array of rowwise pairwise negative quadrant dependent random variables |
| Keyword:
|
complete convergence |
| Keyword:
|
dependent bootstrap |
| Keyword:
|
sequence of i.i.d.\ random variables |
| MSC:
|
60F15 |
| MSC:
|
62F40 |
| MSC:
|
62G09 |
| idZBL:
|
Zbl 06486910 |
| idMR:
|
MR3419961 |
| DOI:
|
10.1007/s10492-015-0094-6 |
| . |
| Date available:
|
2015-05-15T07:36:25Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144262 |
| . |
| Reference:
|
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