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Optimal sequential multiple hypothesis testing in presence of control variables
Kybernetika, Tome 45 (2009) no. 3, pp. 507-528 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $.
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 $.
Classification : 60G40, 62C99, 62L10, 62L15, 93E20
Keywords: sequential analysis; sequential hypothesis testing; multiple hypotheses; control variable; independent observations; optimal stopping; optimal control; optimal decision; optimal sequential testing procedure; Bayes; sequential probability ratio test 
@article{KYB_2009_45_3_a9,
     author = {Novikov, Andrey},
     title = {Optimal sequential multiple hypothesis testing in presence of control variables},
     journal = {Kybernetika},
     pages = {507--528},
     year = {2009},
     volume = {45},
     number = {3},
     mrnumber = {2543137},
     zbl = {1165.62053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009_45_3_a9/}
}
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Novikov, Andrey. Optimal sequential multiple hypothesis testing in presence of control variables. Kybernetika, Tome 45 (2009) no. 3, pp. 507-528. http://geodesic.mathdoc.fr/item/KYB_2009_45_3_a9/

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