标题： 存在控制变量的序贯多重假设检验 显示英文标题

标题： Sequential multiple hypothesis testing in presence of control variables

摘要： 假设在统计实验的任一阶段，都可以使用一个影响观测数据 $X$ 分布的控制变量 $Y$。 $Y$的分布取决于某个未知参数$\theta$，我们考虑在以下序贯背景下，允许数据受$X$控制时，检验多重假设$H_1: \theta=\theta_1$，$H_2: \theta=\theta_2, ...$，$H_k: \theta=\theta_k$的问题。 实验从将一个值$X_1$分配给控制变量并观察响应$Y_1$开始。 经过一些分析后，选择另一个控制变量的值$X_2$，并观察响应$Y_2$，等等。 假设实验最终停止，此时需要对其中一个假设$H_1,...$、$H_k$做出最终决定。 本文的目的是刻画在如下情形下基于这类实验所获得数据的最优序贯检验程序的结构：当观测值$Y_1, Y_2,..., Y_n$在给定控制变量$X_1,X_2,..., X_n$,$n=1,2,...$时相互独立。 显示英文摘要

摘要： 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 $H_1: \theta=\theta_1$, $H_2: \theta=\theta_2, ...$, $H_k: \theta=\theta_k$ 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 $H_1,...$, $H_k$ 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 $Y_1, Y_2,..., Y_n$ are independent, given controls $X_1,X_2,..., X_n$, $n=1,2,...$.