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Optimal sequential testing of two simple hypotheses in presence of control variables

7 December 2008
A. Novikov
ArXiv (abs)PDFHTML
Abstract

Suppose that at any stage of a statistical experiment a control variable XXX that affects the distribution of the observed data YYY can be used. The distribution of YYY depends on some unknown parameter θ\thetaθ, and we consider the classical problem of testing a simple hypothesis H0:θ=θ0H_0: \theta=\theta_0H0​:θ=θ0​ against a simple alternative H1:θ=θ1H_1: \theta=\theta_1H1​:θ=θ1​ allowing the data to be controlled by XXX, in the following sequential context. The experiment starts with assigning a value X1X_1X1​ to the control variable and observing Y1Y_1Y1​ as a response. After some analysis, we choose another value X2X_2X2​ for the control variable, and observe Y2Y_2Y2​ as a response, etc. It is supposed that the experiment eventually stops, and at that moment a final decision in favour of H0H_0H0​ or H1H_1H1​ is to be taken. In this article, our aim is to characterize the structure of optimal sequential procedures, based on this type of data, for testing a simple hypothesis against a simple alternative.

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