如果进行认识论解释，计算出的95%置信区间确实以0.95的概率覆盖真值

The case for balanced hypothesis tests and equal-tailed confidence intervals

Introduction: there is an ongoing debate about directional inference of two-sided hypothesis tests for which some authors argue that rejecting $θ= θ_0$ does not allow to conclude that $θ> θ_0$ or $θ< θ_0$ but only that $θ\neq θ_0$, while others argue that this is a minor error without practical consequence. Discussion: new elements are brought to the debate. It is shown that the directional interpretation of some non-directional hypothesis tests about Receiver Operating Characteristic (ROC) and survival curves may lead to inflated type III error rates with a probability of concluding that a di…

Deciding with Judgment

A decision maker starts from a judgmental decision and moves to the closest boundary of the confidence interval. This statistical decision rule is admissible and does not perform worse than the judgmental decision with a probability equal to the confidence level, which is interpreted as a coefficient of statistical risk aversion. The confidence level is related to the decision maker's aversion to uncertainty and can be elicited with laboratory experiments using urns a la Ellsberg. The decision rule is applied to a problem of asset allocation for an investor whose judgmental decision is to keep…

决策树中分裂点的置信集

Confidence sets for split points in decision trees

本文研究了在决策树（CART）中寻找分裂点置信集的问题。我们的主要结果建立了渐近分布的最小二乘估计和一些相关的残差平方和统计量的二进制决策树逼近光滑的回归曲线。涉及非正态极限分布的立方根渐近性。我们研究了各种置信度集的分裂点，一个校准使用二次抽样引导，和其他校准使用插件估计的一些冗余参数。在模拟研究中的信心集的性能进行评估。开发这样的信心集的动机来自于大沼泽地的磷污染问题。生态学家认为，分裂点提供了一个磷阈值，在生物失衡发生时，置信集的下端点可以解释为一个水平，是生态系统的保护。杜克大学湿地中心在大沼泽地进行的磷剂量研究的数据说明了这一点。

通过随机Weierstrass型算子得到的分布函数及其导数的显式置信带和置信区间

Explicit confidence bands and intervals for distribution functions and their derivatives via random Weierstrass-type operators

将二阶经典核估计解释为随机Weierstrass型算子，在仅假设导数一致连续或存在第一类间断点时，利用Dvoretzky-Kiefer-Wolfowitz不等式和浓度不等式，构造分布函数及其导数的显式非渐近置信带和置信区间，长度依赖于光滑度。

置信分布中的点质量：是缺点还是优点？

Point Mass in the Confidence Distribution: Is it a Drawback or an Advantage?

本文证明置信分布中的点质量是优点而非缺点，它能维持置信区间覆盖概率，优于和谐信念等方法，并揭示置信特征才是克服概率推断缺陷的关键。

Frequentist Inference without Repeated Sampling

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random phenomena are interpreted as classical probabilities, and this interpretation is applied to statistical inference using urn models. Both classical and limiting relative frequency interpretations can be used to communicate statistical inference, and the effectiveness of each is discussed. Recent descriptions of p-values, confidence intervals, and power are vie…