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高维数据中被选参数的经验贝叶斯置信区间AI 解读

Modern statistical problems often involve a large number of populations and hence a large number of parameters that characterize these populations. It is common for scientists to use data to select the most significant populations, such as those with the largest t statistics. The scientific interest often lies in studying and making inferences regarding these parameters, called the selected parameters, corresponding to the selected populations. The current statistical…

控制错误覆盖率的经验贝叶斯置信区间AI 解读

Summary Benjamini and Yekutieli suggested that it is important to account for multiplicity correction for confidence intervals when only some of the selected intervals are reported. They introduced the concept of the false coverage rate (FCR) for confidence intervals which is parallel to the concept of the false discovery rate in the multiple-hypothesis testing problem and they developed confidence intervals for selected parameters which control the FCR. Their approach…

同时收缩均值与方差的经验贝叶斯置信区间AI 解读

Summary We construct empirical Bayes intervals for a large number p of means. The existing intervals in the literature assume that variances σi2 are either equal or unequal but known. When the variances are unequal and unknown, the suggestion is typically to replace them by unbiased estimators Si2. However, when p is large, there would be advantage in ‘borrowing strength’ from each other. We derive double-shrinkage intervals for means on the basis of our empirical Bayes…

具有阈值化性质的极小极大估计及其小波分析应用AI 解读

Many statistical practices involve choosing between a full model and reduced models where some coefficients are reduced to zero. Data were used to select a model with estimated coefficients. Is it possible to do so and still come up with an estimator always better than the traditional estimator based on the full model? The James–Stein estimator is such an estimator, having a property called minimaxity. However, the estimator considers only one reduced model, namely the…

预测区间、因子分析模型与高维经验线性预测AI 解读

We discuss a technique that provides prediction intervals based on a model called an empirical linear model. The technique, high-dimensional empirical linear prediction (HELP), involves principal component analysis, factor analysis and model selection. In fact, a special case of the empirical model is the factor analysis model. A factor analysis model does not generally aim at prediction, however. Therefore, HELP can be viewed as a technique that provides prediction (and…

生物等效性问题的无偏检验AI 解读

It is shown that the standard two one-sided tests procedure for bioequivalence is a biased test. Better tests exist. In this paper, an unbiased $\alpha$-level test and other tests which are uniformly more powerful than the two one-sided tests procedure are constructed. Its power can be noticeably larger than that of the $\alpha$-level two one-sided tests procedure.

人工神经网络的预测区间AI 解读

The artificial neural network (ANN) is becoming a very popular model for engineering and scientific applications. Inspired by brain architecture, artificial neural networks represent a class of nonlinear models capable of learning from data. Neural networks have been applied in many areas, including pattern matching, classification, prediction, and process control. This article focuses on the construction of prediction intervals. Previous statistical theory for constructing…

利用先验反馈法进行序约束下的最大似然估计AI 解读

Algorithms for deriving isotonic regression estimators in order-restricted linear models and more generally restricted maximum likelihood estimators are usually quite dependent on the particular problem considered. We propose here an optimization method based on a sequence of formal Bayes estimates whose variances converge to zero. This method, akin to simulated annealing, can be applied “universally”; that is, as long as these Bayes estimators can be derived by exact…

利用先验反馈法进行顺序约束下的极大似然估计AI 解读

Algorithms for deriving isotonic regression estimators in order-restricted linear models and more generally restricted maximum likelihood estimators are usually quite dependent on the particular problem considered. We propose here an optimization method based on a sequence of formal Bayes estimates whose variances converge to zero. This method, akin to simulated annealing, can be applied “universally”; that is, as long as these Bayes estimators can be derived by exact…

最优置信集合、生物等效性与帕斯卡蜗线AI 解读

We begin with a decision-theoretic investigation into confidence sets that minimize expected volume at a given parameter value. Such sets are constructed by inverting a family of uniformly most powerful tests, and hence they also enjoy the optimality property of being uniformly most accurate. In addition, these sets possess Bayesian optimal volume properties and represent the first case (to our knowledge) of a frequentist 1 – α confidence set that possesses a Bayesian…

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序约束下的置信区间估计AI 解读

This article deals with the construction of confidence intervals when the components of the location parameter $\mu$ of the random variable $\mathbf{X}$, which is elliptically symmetrically distributed, are subject to order restrictions. Several domination results are proved by studying the derivative of the coverage probability of the confidence intervals centered at the improved point estimators. Consequently, we strengthen the previously known results regarding the simple…

与生物等效性检验相关的置信区间AI 解读

Previously, the connection between bioequivalence tests and their associated confidence intervals was not well understood. In fact, the α-level two one-sided tests approach was thought to be associated with a 1−2α confidence interval. In this paper, we build up connections which allow us to construct 1−α confidence intervals from α-level tests and vice versa. When applied to the α-level two one-sided tests, the resultant 1−-α confidence intervals are properly contained in…