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多个处理与对照比较的近似似然比检验AI 解读

Some parametric tests for comparing several treatments to a control are examined. Those tests developed earlier tend to rest on a single principle: Simplicity or power; those developed later attempt to fill the gap. We propose a new test that represents another such attempt. The basic idea is to find a simple statistic that is a good approximation to the likelihood ratio statistic. This leads to a power function similar to that of the likelihood ratio test, which is optimal…

比较多个处理与对照的近似似然比检验AI 解读

Some parametric tests for comparing several treatments to a control are examined. Those tests developed earlier tend to rest on a single principle: Simplicity or power; those developed later attempt to fill the gap. We propose a new test that represents another such attempt. The basic idea is to find a simple statistic that is a good approximation to the likelihood ratio statistic. This leads to a power function similar to that of the likelihood ratio test, which is optimal…

单侧多变量问题中一致更有功效的检验AI 解读

We consider a testing problem in which a normal mean vector is at the origin under the null hypothesis and in a cone under the alternative and the covariance matrix is unknown. Perlman studied the likelihood ratio (LR) test and found that it is biased and hence does not compare favorably with Hotelling's T2. We point out that certain tests of Perlman are uniformly more powerful as well as simpler than the LR test. These are the corresponding LR tests when the alternative is…

单侧多元检验问题中一致更强的检验AI 解读

We consider a testing problem in which a normal mean vector is at the origin under the null hypothesis and in a cone under the alternative and the covariance matrix is unknown. Perlman studied the likelihood ratio (LR) test and found that it is biased and hence does not compare favorably with Hotelling's T2. We point out that certain tests of Perlman are uniformly more powerful as well as simpler than the LR test. These are the corresponding LR tests when the alternative is…

一致范数偏离模型下的极小极大回归设计AI 解读

Model robustness in optimal regression design is studied by introducing a family of nonparametric models, which are defined as neighborhoods of classical parametric models in terms of the uniform norm. Optimal designs are sought under a minimax criterion for estimating linear functionals on such models that may be put as integrals using measures of finite support. A set of conditions equivalent to design optimality is derived using a Lagrangian principle applicable when the…

多终点下关于指定处理的假设检验AI 解读

The problem of comparing an identified treatment with K other treatments is considered in a multivariate setting. Many formulations of composite alternative hypotheses are possible. For example, one might wish to examine whether the identified treatment is superior to the other treatments on all components of the response vector (i.e., is uniformly best) or whether the identified treatment is better than each treatment on at least one component (i.e., is admissible). For…

多个终点下针对指定处理的假设检验AI 解读

The problem of comparing an identified treatment with K other treatments is considered in a multivariate setting. Many formulations of composite alternative hypotheses are possible. For example, one might wish to examine whether the identified treatment is superior to the other treatments on all components of the response vector (i.e., is uniformly best) or whether the identified treatment is better than each treatment on at least one component (i.e., is admissible). For…

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非负分量正态均值向量的近似似然比检验及临床试验应用AI 解读

A new multivariate statistic, designed to be sensitive to the alternative hypothesis that a mean vector lies in the positive orthant, rather than to all alternatives or to alternatives on a line (O'Brien, 1984), is proposed. The statistic is shown to approximate the likelihood ratio test statistic for such alternatives (Kudô, 1963; Perlman, 1969). Its null distribution is a special case of the chi-bar-squared distribution, which allows critical values to be obtained. Such a…