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用于快速准确经验似然推断的变分贝叶斯AI 解读

We develop a fast and accurate approach to approximate posterior distributions in the Bayesian empirical likelihood framework. Bayesian empirical likelihood allows for the use of Bayesian shrinkage without specification of a full likelihood but is notorious for leading to several computational difficulties. By coupling the stochastic variational Bayes procedure with an adjusted empirical likelihood framework, the proposed method overcomes the intractability of both the exact…

基于模型拟合度先验的贝叶斯回归：R2-D2 收缩先验AI 解读

Prior distributions for high-dimensional linear regression require specifying a joint distribution for the unobserved regression coefficients, which is inherently difficult. We instead propose a new class of shrinkage priors for linear regression via specifying a prior first on the model fit, in particular, the coefficient of determination, and then distributing through to the coefficients in a novel way. The proposed method compares favorably to previous approaches in terms…

存在非随机缺失的牙周数据非参数空间模型AI 解读

Periodontal disease progression is often quantified by clinical attachment level (CAL) defined as the distance down a tooth's root that is detached from the surrounding bone. Measured at 6 locations per tooth throughout the mouth (excluding the molars), it gives rise to a dependent data set-up. These data are often reduced to a one-number summary, such as the whole mouth average or the number of observations greater than a threshold, to be used as the response in a…

通过两阶段广义经验似然实现高效稳健回归AI 解读

Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we develop and study a linear regression estimator that comes close. Efficiency obtains from the estimator's close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated sum of (weighted) squared residuals. We prove maximum attainable finite-sample…

基于惩罚可信区域的一致高维贝叶斯变量选择AI 解读

For high-dimensional data, particularly when the number of predictors greatly exceeds the sample size, selection of relevant predictors for regression is a challenging problem. Methods such as sure screening, forward selection, or penalized regressions are commonly used. Bayesian variable selection methods place prior distributions on the parameters along with a prior over model space, or equivalently, a mixture prior on the parameters having mass at zero. Since exhaustive…

用于无模型变量选择的收缩逆回归估计AI 解读

Summary The family of inverse regression estimators that was recently proposed by Cook and Ni has proven effective in dimension reduction by transforming the high dimensional predictor vector to its low dimensional projections. We propose a general shrinkage estimation strategy for the entire inverse regression estimation family that is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimators achieve consistency in variable…

Logistic 回归模型的最小距离估计AI 解读

It is well known that the maximum likelihood fit of the logistic regression parameters can be greatly affected by atypical observations. Several robust alternatives have been proposed. However, if we consider the model from the case-control viewpoint, it is clear that current techniques can exhibit poor behaviour in many common situations. A new robust class of estimation procedures is introduced. The estimators are constructed via a minimum distance approach after…