TY - JOUR AU - Novikov, Andrey TI - Optimal sequential multiple hypothesis testing in presence of control variables JO - Kybernetika PY - 2009 PB - Institute of Information Theory and Automation AS CR VL - 45 IS - 3 SP - 507 EP - 528 AB - 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. , Y n are independent, given controls X 1, X 2. 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. It is supposed that the experiment eventually stops, and at that moment a final decision in favor of one of the hypotheses H 1. After some analysis, another value X 2 for the control variable is chosen, and Y 2 as a response is observed, etc. The experiment starts with assigning a value X 1 to the control variable and observing Y 1 as a response. , H k : θ = θ k allowing the data to be controlled by X, in the following sequential context. The distribution of Y depends on some unknown parameter θ, and we consider the problem of testing multiple hypotheses H 1 : θ = θ 1, H 2 : θ = θ 2. 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. Optimal sequential multiple hypothesis testing in presence of control variables
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