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剂量反应与毒性研究中无需多重性调整的逐步置信区间AI 解读

Not all simultaneous inferences need multiplicity adjustment. If the sequence of individual inferences is predefined, and failure to achieve the desired inference at any step renders subsequent inferences unnecessary, then multiplicity adjustment is not needed. This can be justified using the closed testing principle to test appropriate hypotheses that are nested in sequence, starting with the most restrictive one. But what hypotheses are appropriate may not be obvious in…

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关于线性不等式假设的一致更有力单侧检验AI 解读

Let $\mathbf{X}$ have a multivariate, $p$-dimensional normal distribution $(p \geq 2)$ with unknown mean $\mathbf{\mu}$ and known, nonsingular covariance $\mathbf{\Sigma}$. Consider testing $H_0: \mathbf{b}'_i\mathbf{\mu} \leq 0$, for some $i = 1, \ldots, k$, versus $H_1: \mathbf{b}'_i\mathbf{\mu} > 0$, for all $i = 1, \ldots, k$, where $\mathbf{b}_1, \ldots, \mathbf{b}_k, k \geq 2$, are known vectors that define the hypotheses. For any $0 < \alpha < 1/2$, we construct a…

基于选择性二项信息的估计：如何解读被挑选的击球率AI 解读

Often sports announcers, particularly in baseball, provide the listener with exaggerated information concerning a player's performance. For example, we may be told that Dave Winfield, a popular baseball player, has hit safely in 8 of his last 17 chances (a batting average of .471). This is biased, or selected information, as the “17” was chosen to maximize the reported percentage. We model this as observing a maximum success rate of a Bernoulli process and show how to…

在干扰参数置信集合上最大化的 p 值AI 解读

For testing problems of the form H 0: v = v 0 with unknown nuisance parameter θ, various methods are used to deal with θ. The simplest approach is exemplified by the t test where the unknown variance is replaced by the sample variance and the t distribution accounts for estimation of the variance. In other problems, such as the 2 × 2 contingency table, one conditions on a sufficient statistic for 0 and proceeds as in Fisher's exact test. Because neither of these standard…

选择性二项信息下的估计：如何理解被挑选的棒球打击率AI 解读

Often sports announcers, particularly in baseball, provide the listener with exaggerated information concerning a player's performance. For example, we may be told that Dave Winfield, a popular baseball player, has hit safely in 8 of his last 17 chances (a batting average of .471). This is biased, or selected information, as the “17” was chosen to maximize the reported percentage. We model this as observing a maximum success rate of a Bernoulli process and show how to…

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正态均值线性不等式假设的一致更强检验AI 解读

This article considers some hypothesis-testing problems regarding normal means. In these problems, the hypotheses are defined by linear inequalities on the means. We show that in certain problems the likelihood ratio test (LRT) is not very powerful. We describe a test that has the same size, α, as the LRT and is uniformly more powerful. The test is easily implemented, since its critical values are standard normal percentiles. The increase in power with the new test can be…