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固定 b 子抽样与区块自助法：基于 p 值校准的改进置信集AI 解读

Summary Subsampling and block-based bootstrap methods have been used in a wide range of inference problems for time series. To accommodate the dependence, these resampling methods involve a bandwidth parameter, such as the subsampling window width and block size in the block-based bootstrap. In empirical work, using different bandwidth parameters could lead to different inference results, but traditional first-order asymptotic theory does not capture the choice of the…

针对缺失值与观察性研究进行处理前变量调整的Mann–Whitney检验AI 解读

Summary The conventional Wilcoxon or Mann–Whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies. This is because the missingness of the outcomes or the participation in the treatments may depend on certain pretreatment variables. We propose an approach to adjust the Mann–Whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the…

函数型时间序列的均值估计与两样本检验AI 解读

Summary The paper is concerned with inference based on the mean function of a functional time series. We develop a normal approximation for the functional sample mean and then focus on the estimation of the asymptotic variance kernel. Using these results, we develop and asymptotically justify testing procedures for the equality of means in two functional samples exhibiting temporal dependence. Evaluated by means of a simulation study and application to a real data set, these…

带错误控制的变量选择：再论稳定性选择AI 解读

Summary Stability selection was recently introduced by Meinshausen and Bühlmann as a very general technique designed to improve the performance of a variable selection algorithm. It is based on aggregating the results of applying a selection procedure to subsamples of the data. We introduce a variant, called complementary pairs stability selection, and derive bounds both on the expected number of variables included by complementary pairs stability selection that have low…

时空模型中的联合复合估计函数AI 解读

Summary Modelling of spatiotemporal processes has received considerable attention in recent statistical research. However, owing to the high dimensionality of the data, the joint modelling of spatial and temporal processes presents a great computational challenge, in both likelihood-based and Bayesian approaches. We propose a joint composite estimating function approach to estimating spatiotemporal covariance structures. This substantially reduces the computational…

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…

基于序数优势曲线的随机有序分布推断AI 解读

Summary In a variety of applications researchers collect data that are sampled under ordered experimental conditions. In such situations it is reasonable to assume that outcomes are ordered stochastically by the level of the treatment. For example a toxicologist may want to assess the effect of a toxin on the reproductive system by studying the number of offspring produced by an animal as a function of the dose that it received. A variety of scientific questions arise in…

相关追踪：指数模型的前向逐步变量选择AI 解读

Summary A stepwise procedure, correlation pursuit (COP), is developed for variable selection under the sufficient dimension reduction framework, in which the response variable Y is influenced by the predictors X1,X2,…,Xp through an unknown function of a few linear combinations of them. Unlike linear stepwise regression, COP does not impose a special form of relationship (such as linear) between the response variable and the predictor variables. The COP procedure selects…

超高维数据中稀疏区段的稳健检测与识别AI 解读

Summary Copy number variants (CNVs) are alternations of DNA of a genome that result in the cell having less or more than two copies of segments of the DNA. CNVs correspond to relatively large regions of the genome, ranging from about one kilobase to several megabases, that are deleted or duplicated. Motivated by CNV analysis based on next generation sequencing data, we consider the problem of detecting and identifying sparse short segments hidden in a long linear sequence of…

概率指数模型AI 解读

Summary We present a semiparametric statistical model for the probabilistic index which can be defined as P(Y⩽Y*), where Y and Y* are independent random response variables associated with covariate patterns X and X* respectively. A link function defines the relationship between the probabilistic index and a linear predictor. Asymptotic normality of the estimators and consistency of the covariance matrix estimator are established through semiparametric theory. The model is…

高维分类之路：正则化最优仿射判别方法AI 解读

Summary For high dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and accumulation of noise. Therefore, researchers proposed independence rules to circumvent the diverging spectra, and sparse independence rules to mitigate the issue of accumulation of noise. However, in biological applications, often a group of correlated genes are responsible for clinical outcomes, and the use of…

可转置数据的推断：行列相关性的建模AI 解读

Summary We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Many of these data matrices are transposable meaning that neither the row variables nor the column variables can be considered independent instances. An example of this scenario is detecting significant genes in microarrays when the samples may be dependent because of latent variables or unknown batch effects. By modelling this matrix data by using the…

对称正定矩阵的局部多项式回归AI 解读

Summary Local polynomial regression has received extensive attention for the non-parametric estimation of regression functions when both the response and the covariate are in Euclidean space. However, little has been done when the response is in a Riemannian manifold. We develop an intrinsic local polynomial regression estimate for the analysis of symmetric positive definite matrices as responses that lie in a Riemannian manifold with covariate in Euclidean space. The…

通过更早切换加快追赶：自适应估计与 AIC–BIC 困境AI 解读

Summary Prediction and estimation based on Bayesian model selection and model averaging, and derived methods such as the Bayesian information criterion BIC, do not always converge at the fastest possible rate. We identify the catch-up phenomenon as a novel explanation for the slow convergence of Bayesian methods, which inspires a modification of the Bayesian predictive distribution, called the switch distribution. When used as an adaptive estimator, the switch distribution…

从领头变量中学习：LOL 高维回归方法AI 解读

Summary The paper investigates the estimation problem in a regression-type model. To be able to deal with potential high dimensions, we provide a procedure called LOL—for learning out of leaders—with no optimization step. LOL is an autodriven algorithm with two thresholding steps. A first adaptive thresholding helps to select leaders among the initial regressors to obtain a first reduction of dimensionality. Then a second thresholding is performed on the linear regression on…

通过倾斜相关进行高维变量选择AI 解读

Summary The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly spurious) high correlations between the variables, which result in marginal correlation being unreliable as a measure of association between the variables and the response. We propose a new way of measuring the contribution of each…

环境序列样本的系统发育 Kantorovich–Rubinstein 距离AI 解读

Summary It is now common to survey microbial communities by sequencing nucleic acid material extracted in bulk from a given environment. Comparative methods are needed that indicate the extent to which two communities differ given data sets of this type. UniFrac, which gives a somewhat ad hoc phylogenetics-based distance between two communities, is one of the most commonly used tools for these analyses. We provide a foundation for such methods by establishing that, if we…

极值建模中阈值诊断与不确定性的似然方法AI 解读

Summary For extreme value modelling based on threshold techniques, a well-documented issue is the sensitivity of inference from the model to the choice of threshold. The threshold above which we assume a non-homogeneous Poisson process, or equivalently generalized Pareto representation, to be a reasonable approximation to the distribution is traditionally selected before analysis and subsequently treated as fixed and known. In doing so, the analyst cannot account for the…

对数据选择后参数的调整贝叶斯推断AI 解读

Summary We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that providing Bayesian inference for selected parameters is a truncated data problem. We show that if the prior for the parameter is non-informative, or if the parameter is a ‘fixed’ unknown constant, then it is necessary to adjust the…

局部收缩规则、Lévy 过程与正则化回归AI 解读

Summary We use Lévy processes to generate joint prior distributions, and therefore penalty functions, for a location parameter β=(β1,…,βp) as p grows large. This generalizes the class of local–global shrinkage rules based on scale mixtures of normals, illuminates new connections between disparate methods and leads to new results for computing posterior means and modes under a wide class of priors. We extend this framework to large-scale regularized regression problems where…

充分原因交互作用的半参数检验AI 解读

Summary A sufficient cause interaction between two exposures signals the presence of individuals for whom the outcome would occur only under certain values of the two exposures. When the outcome is dichotomous and all exposures are categorical, then, under certain no confounding assumptions, empirical conditions for sufficient cause interactions can be constructed on the basis of the sign of linear contrasts of conditional outcome probabilities between differently exposed…

实现函数型数据的近乎完美分类AI 解读

Summary We show that, in functional data classification problems, perfect asymptotic classification is often possible, making use of the intrinsic very high dimensional nature of functional data. This performance is often achieved by linear methods, which are optimal in important cases. These results point to a marked contrast between classification for functional data and its counterpart in conventional multivariate analysis, where the dimension is kept fixed as the sample…

具有稀疏奇异值分解的降秩随机回归AI 解读

Summary For a reduced rank multivariate stochastic regression model of rank r*, the regression coefficient matrix can be expressed as a sum of r* unit rank matrices each of which is proportional to the outer product of the left and right singular vectors. For improving predictive accuracy and facilitating interpretation, it is often desirable that these left and right singular vectors be sparse or enjoy some smoothness property. We propose a regularized reduced rank…

Lasso类问题中剔除预测变量的强规则AI 解读

Summary We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui and his colleagues have proposed ‘SAFE’ rules, based on univariate inner products between each predictor and the outcome, which guarantee that a coefficient will be 0 in the solution vector. This provides a reduction in the number of variables that need to be entered into the optimization. We propose strong rules that are very simple and yet…