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一族贝叶斯多重检验程序AI 解读

Under the model of independent test statistics, we propose a two-parameter family of Bayes multiple testing procedures. The two parameters can be viewed as tuning parameters. Using the Benjamini–Hochberg step-up procedure for controlling false discovery rate as a baseline for conservativeness, we choose the tuning parameters to compromise between the operating characteristics of that procedure and a less conservative procedure that focuses on alternatives that a priori might…

锥序关联、随机锥排序及其在序约束检验中的应用AI 解读

Cohen, Sackrowitz and Samuel-Cahn introduced the notion of cone order association and established a necessary and sufficient condition for a normal random vector to be cone order associated (COA). In this paper we provide the following: (1) a necessary and sufficient condition for a multinomial distribution to be COA when the cone is a pairwise contrast cone; (2) a relationship between COA and regular association; (3) a notion of stochastic cone ordering (SCO) of random…

利用先导样本构造置信下界及其审计应用AI 解读

A pilot study is often done prior to a more thorough study, to determine whether a larger-scale effort is likely to yield useful results. In one sense, the pilot study can discourage or encourage further investigation. This is true in many situations in auditing. For example, an auditor seeks to determine that amount an insurance provider overpays. Often the provider makes few mistakes and overpays little. On the other hand, occasionally a provider overpays a lot. Because…

利用先导样本构造置信下界及其审计应用AI 解读

A pilot study is often done prior to a more thorough study, to determine whether a larger-scale effort is likely to yield useful results. In one sense, the pilot study can discourage or encourage further investigation. This is true in many situations in auditing. For example, an auditor seeks to determine that amount an insurance provider overpays. Often the provider makes few mistakes and overpays little. On the other hand, occasionally a provider overpays a lot. Because…

指数族回归中的无偏检验AI 解读

Let $(X_{ij}, \mathbf{z}_i), i = 1, 2, \ldots, k, j = 1, 2, \ldots, n_i$, be independent observations such that $\mathbf{z}_i$ is a fixed $r \times 1$ vector $\lbrack r$ can be 0 (no $\mathbf{z}$'s observed) or $1, 2, \ldots, k - 1\rbrack$, and $X_{ij}$ is distributed according to a one-parameter exponential family which is log concave with natural parameter $\theta_i$. We test the hypothesis that $\theta = \mathbf{Z}\beta$, where $\theta = (\theta_1, \ldots, \theta_k)', \mathbf{Z}$…

模型选择后推断：变换型与自适应推断的决策论方法AI 解读

A decision-theory approach is formulated for inference following model selection. Inference here refers to either testing, point estimation, or confidence estimation. The loss function includes components for model selection as well as for inference and allows for flexibility in emphasis on one or the other, if such emphasis is desired. A general prescription for Bayes and generalized Bayes procedures is given. A procedure consists of model selection and inference. The…

等单元概率情形下卡方、似然比及其他拟合优度检验的无偏性AI 解读

The chi-square test, likelihood ratio test, and other goodness of fit tests in a family are shown to have monotonic power functions, and hence are unbiased, for testing a simple hypothesis that all cell probabilities are equal. The chi-square test is also shown to be Type D for this situation.