论文检索

基于 F 建模的方差经验贝叶斯估计AI 解读

Summary We consider the problem of empirical Bayes estimation of multiple variances when provided with sample variances. Assuming an arbitrary prior on the variances, we derive different versions of the Bayes estimators using different loss functions. For one particular loss function, the resulting Bayes estimator relies on the marginal cumulative distribution function of the sample variances only. When replacing it with the empirical distribution function, we obtain an…

利用高斯镜像控制错误发现率AI 解读

Simultaneously, finding multiple influential variables and controlling the false discovery rate (FDR) for linear regression models is a fundamental problem. We here propose the Gaussian Mirror (GM) method, which creates for each predictor variable a pair of mirror variables by adding and subtracting a randomly generated Gaussian perturbation, and proceeds with a certain regression method, such as the ordinary least-square or the Lasso (the mirror variables can also be…

基于 Lasso 的稀疏切片逆回归AI 解读

For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if $ρ = \mathrm{lim} \frac{p}{n} = 0$, where p is the dimension and n is the sample size. Thus, when p is of the same or a higher order of n, additional assumptions such as sparsity must be imposed in order to ensure consistency for SIR. By constructing artificial response variables made up from…

高维切片逆回归的一致性与稀疏性AI 解读

We provide here a framework to analyze the phase transition phenomenon of slice inverse regression (SIR), a supervised dimension reduction technique introduced by Li [J. Amer. Statist. Assoc. 86 (1991) 316–342]. Under mild conditions, the asymptotic ratio $\rho=\lim p/n$ is the phase transition parameter and the SIR estimator is consistent if and only if $\rho=0$. When dimension $p$ is greater than $n$, we propose a diagonal thresholding screening SIR (DT-SIR) algorithm.…

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…