| Title:
|
Comparing the distributions of sums of independent random vectors (English) |
| Author:
|
Gordienko, Evgueni |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
[519]-529 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(X_n, n\ge 1), (\tilde{X}_n, n\ge 1)$ be two sequences of i.i.d. random vectors with values in ${\mathbb{R}}^k$ and $S_n=X_1+\cdots +X_n$, $\tilde{S}_n=\tilde{X}_1+\cdots +\tilde{X}_n$, $n\ge 1$. Assuming that $EX_1=E\tilde{X}_1$, $E|X_1|^2<\infty $, $E|\tilde{X}_1|^{k+2}<\infty $ and the existence of a density of $\tilde{X}_1$ satisfying the certain conditions we prove the following inequalities: \[v(S_n,\tilde{S}_n)\le c\;\max \big \lbrace v(X_1,\tilde{X}_1), \zeta _2(X_1,\tilde{X}_1)\big \rbrace , \quad n=1,2,\dots ,\] where $v$ and $\zeta _2$ are the total variation and Zolotarev’s metrics, respectively. (English) |
| Keyword:
|
sum of random vectors |
| Keyword:
|
the total variation distance |
| Keyword:
|
bound of closeness |
| Keyword:
|
Zolotarev’s metric |
| Keyword:
|
characteristic function |
| MSC:
|
60F99 |
| MSC:
|
60G50 |
| idZBL:
|
Zbl 1249.60086 |
| idMR:
|
MR2180360 |
| . |
| Date available:
|
2009-09-24T20:10:48Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135672 |
| . |
| Reference:
|
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| . |
