| Title:
|
Optimal sequential multiple hypothesis testing in presence of control variables (English) |
| Author:
|
Novikov, Andrey |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
507-528 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ at this stage can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the problem of testing multiple hypotheses $H_1:\,\theta=\theta_1$, $H_2:\,\theta=\theta_2, \ldots $, $H_k:\,\theta=\theta_k$ allowing the data to be controlled by $X$, in the following sequential context. The experiment starts with assigning a value $X_1$ to the control variable and observing $Y_1$ as a response. After some analysis, another value $X_2$ for the control variable is chosen, and $Y_2$ as a response is observed, etc. It is supposed that the experiment eventually stops, and at that moment a final decision in favor of one of the hypotheses $H_1,\ldots $, $H_k$ is to be taken. In this article, our aim is to characterize the structure of optimal sequential testing procedures based on data obtained from an experiment of this type in the case when the observations $Y_1, Y_2,\ldots , Y_n$ are independent, given controls $X_1,X_2,\ldots , X_n$, $n=1,2,\ldots $. (English) |
| Keyword:
|
sequential analysis |
| Keyword:
|
sequential hypothesis testing |
| Keyword:
|
multiple hypotheses |
| Keyword:
|
control variable |
| Keyword:
|
independent observations |
| Keyword:
|
optimal stopping |
| Keyword:
|
optimal control |
| Keyword:
|
optimal decision |
| Keyword:
|
optimal sequential testing procedure |
| Keyword:
|
Bayes |
| Keyword:
|
sequential probability ratio test |
| MSC:
|
60G40 |
| MSC:
|
62C99 |
| MSC:
|
62L10 |
| MSC:
|
62L15 |
| MSC:
|
93E20 |
| idZBL:
|
Zbl 1165.62053 |
| idMR:
|
MR2543137 |
| . |
| Date available:
|
2010-06-02T18:46:24Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140020 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| . |
