| Title:
|
Stability estimating in optimal sequential hypotheses testing (English) |
| Author:
|
Gordienko, Evgueni |
| Author:
|
Novikov, Andrey |
| Author:
|
Zaitseva, Elena |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
331-344 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations $X_1,X_2,\dots$ when testing two simple hypotheses about their common density $f$: $f=f_0$ versus $f=f_1$. As a functional to be minimized, it is used a weighted sum of the average (under $f_0$) sample number and the two types error probabilities. We prove that the problem is reduced to stopping time optimization for a ratio process generated by $X_1,X_2,\dots$ with the density $f_0$. For $\tau_*$ being the corresponding optimal stopping time we consider a situation when this rule is applied for testing between $f_0$ and an alternative $\tilde f_1$, where $\tilde f_1$ is some approximation to $f_1$. An inequality is obtained which gives an upper bound for the expected cost excess, when $\tau_*$ is used instead of the rule $\tilde\tau_*$ optimal for the pair $(f_0,\tilde f_1)$. The inequality found also estimates the difference between the minimal expected costs for optimal tests corresponding to the pairs $(f_0,f_1)$ and $(f_0,\tilde f_1)$. (English) |
| Keyword:
|
sequential hypotheses test |
| Keyword:
|
simple hypothesis |
| Keyword:
|
optimal stopping |
| Keyword:
|
sequential probability ratio test |
| Keyword:
|
likelihood ratio statistic |
| Keyword:
|
stability inequality |
| MSC:
|
62L10 |
| MSC:
|
62L15 |
| idZBL:
|
Zbl 1165.62052 |
| idMR:
|
MR2518155 |
| . |
| Date available:
|
2010-06-02T18:34:21Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140072 |
| . |
| Reference:
|
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| Reference:
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| . |
