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高维回归空间中的多重影响点检测AI 解读

Summary Influence diagnosis is an integrated component of data analysis but has been severely underinvestigated in a high dimensional regression setting. One of the key challenges, even in a fixed dimensional setting, is how to deal with multiple influential points that give rise to masking and swamping effects. The paper proposes a novel group deletion procedure referred to as multiple influential point detection by studying two extreme statistics based on a…

偏倚抽样下二元生存数据的半参数模型AI 解读

Summary To understand better the relationship between patient characteristics and their residual survival after an intermediate event such as the local recurrence of cancer, it is of interest to identify patients with the intermediate event and then to analyse their residual survival data. One challenge in analysing such data is that the observed residual survival times tend to be longer than those in the target population, since patients who die before experiencing the…

不完整数据下分位数估计的一般框架AI 解读

Summary Quantile estimation has attracted significant research interest in recent years. However, there has been only a limited literature on quantile estimation in the presence of incomplete data. We propose a general framework to address this problem. Our framework combines the two widely adopted approaches for missing data analysis, the imputation approach and the inverse probability weighting approach, via the empirical likelihood method. The method proposed is capable…

Summary The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, because of the noise structure, where the noise components of the different co-ordinates of the multi-dimensional process operate on different timescales, standard inference tools are ill conditioned. We propose to use a higher order scheme to approximate the likelihood, such that the different timescales are…

利用局部工具变量曲线进行连续工具变量的稳健因果推断AI 解读

Summary Instrumental variables are commonly used to estimate effects of a treatment afflicted by unmeasured confounding, and in practice instruments are often continuous (e.g. measures of distance, or treatment preference). However, available methods for continuous instruments have important limitations: they either require restrictive parametric assumptions for identification, or else rely on modelling both the outcome and the treatment process well (and require modelling…

确定性平行分析：因子与主成分数量选择的改进方法AI 解读

Summary Factor analysis and principal component analysis are used in many application areas. The first step, choosing the number of components, remains a serious challenge. Our work proposes improved methods for this important problem. One of the most popular state of the art methods is parallel analysis (PA), which compares the observed factor strengths with simulated strengths under a noise-only model. The paper proposes improvements to PA. We first derandomize it,…

未知函数分布相等的综合非参数检验AI 解读

Summary We present a novel family of non-parametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a generalization of the maximum mean discrepancy tests described by Gretton and colleagues, using recent developments from the higher order pathwise differentiability literature. Despite their complex derivation, the associated test…

结构自适应 Benjamini–Hochberg 多重检验算法AI 解读

Summary In multiple-testing problems, where a large number of hypotheses are tested simultaneously, false discovery rate (FDR) control can be achieved with the well-known Benjamini–Hochberg procedure, which a(0, 1]dapts to the amount of signal in the data, under certain distributional assumptions. Many modifications of this procedure have been proposed to improve power in scenarios where the hypotheses are organized into groups or into a hierarchy, as well as other…

稀疏降秩回归中的交叉验证AI 解读

Summary In high dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received much attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison criterion to find the optimal regularization parameters. However, we show that fixing the parameters across all folds may result in an inconsistency issue, and it is more appropriate to cross-validate projection–selection patterns to obtain…

矩条件与贝叶斯非参数方法AI 解读

Summary Models phrased through moment conditions are central to much of modern inference. Here these moment conditions are embedded within a non-parametric Bayesian set-up. Handling such a model is not probabilistically straightforward as the posterior has support on a manifold. We solve the relevant issues, building new probability and computational tools by using Hausdorff measures to analyse them on real and simulated data. These new methods, which involve simulating on a…

一类非线性多元回归模型的 c、L 与 φk 最优设计刻画AI 解读

Summary Optimal designs for multiple-regression models are determined. We consider a general class of non-linear models including proportional hazards models with different censoring schemes, the Poisson and the negative binomial model. For these models we provide a complete characterization of c-optimal designs for all vectors c in the case of a single covariate. For multiple regression with an arbitrary number of covariates, c-optimal designs for certain vectors c are…

适应平滑度与稀疏性的贝叶斯回归树集成AI 解读

Summary Ensembles of decision trees are a useful tool for obtaining flexible estimates of regression functions. Examples of these methods include gradient-boosted decision trees, random forests and Bayesian classification and regression trees. Two potential shortcomings of tree ensembles are their lack of smoothness and their vulnerability to the curse of dimensionality. We show that these issues can be overcome by instead considering sparsity inducing soft decision trees in…

稀疏广义特征值问题：截断 Rayleigh 流的最优统计收敛率AI 解读

Summary The sparse generalized eigenvalue problem (GEP) plays a pivotal role in a large family of high dimensional statistical models, including sparse Fisher’s discriminant analysis, canonical correlation analysis and sufficient dimension reduction. The sparse GEP involves solving a non-convex optimization problem. Most existing methods and theory in the context of specific statistical models that are special cases of the sparse GEP require restrictive structural…

网络形成的随机游走模型与图的序贯蒙特卡洛方法AI 解读

Summary We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by permitting the location of a new edge to depend explicitly on the structure of the graph, but being nonetheless statistically and computationally tractable. In the limit of infinite walk length, the model converges to an extension of…

连续时间捕获—再捕获数据中总体数量的全似然推断AI 解读

Summary Capture–recapture experiments are widely used cost-effective sampling techniques for estimating population sizes or abundances in biology, ecology, demography, epidemiology and reliability studies. For continuous time capture–recapture data, existing estimation methods are based on conditional likelihoods and an inverse weighting estimating equation. The corresponding Wald-type confidence intervals for the abundance may have severe undercoverage, and their lower…

缓解精细分层实验的分析局限AI 解读

Summary Although attractive from a theoretical perspective, finely stratified experiments such as paired designs suffer from certain analytical limitations that are not present in block-randomized experiments with multiple treated and control individuals in each block. In short, when using a weighted difference in means to estimate the sample average treatment effect, the traditional variance estimator in a paired experiment is conservative unless the pairwise average…

相关伪边际方法AI 解读

Summary The pseudomarginal algorithm is a Metropolis–Hastings-type scheme which samples asymptotically from a target probability density when we can only estimate unbiasedly an unnormalized version of it. In a Bayesian context, it is a state of the art posterior simulation technique when the likelihood function is intractable but can be estimated unbiasedly by using Monte Carlo samples. However, for the performance of this scheme not to degrade as the number T of data points…

利用加权经验过程检验非参数回归中的异方差AI 解读

Summary Heteroscedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroscedasticity for the non-parametric regression model with multiple covariates. It is based on a suitable residual-based empirical distribution function. The residuals are constructed by using local polynomial smoothing. Our test statistic involves a ‘detection function’ that can verify heteroscedasticity by exploiting just the…

给定协变量的高维分位数关联网络的错误发现率控制AI 解读

Summary Motivated by gene coexpression pattern analysis, we propose a novel sample quantile contingency (SQUAC) statistic to infer quantile associations conditioning on covariates. It features enhanced flexibility in handling variables with both arbitrary distributions and complex association patterns conditioning on covariates. We first derive its asymptotic null distribution, and then develop a multiple-testing procedure based on the SQUAC statistic to test simultaneously…

高维缺失数据的插补与正则化优化算法及其扩展AI 解读

Summary Missing data are frequently encountered in high dimensional problems, but they are usually difficult to deal with by using standard algorithms, such as the expectation–maximization algorithm and its variants. To tackle this difficulty, some problem-specific algorithms have been developed in the literature, but there still lacks a general algorithm. This work is to fill the gap: we propose a general algorithm for high dimensional missing data problems. The algorithm…

多个矩阵高斯图的估计AI 解读

Summary Matrix-valued data, where the sampling unit is a matrix consisting of rows and columns of measurements, are emerging in numerous scientific and business applications. Matrix Gaussian graphical models are a useful tool to characterize the conditional dependence structure of rows and columns. We employ non-convex penalization to tackle the estimation of multiple graphs from matrix-valued data under a matrix normal distribution. We propose a highly efficient non-convex…

条件异方差时间序列模型的混合分位数回归估计AI 解读

Summary Estimating conditional quantiles of financial time series is essential for risk management and many other financial applications. For time series models with conditional heteroscedasticity, although it is the generalized auto-regressive conditional heteroscedastic (GARCH) model that has the greatest popularity, quantile regression for this model usually gives rise to non-smooth non-convex optimization which may hinder its practical feasibility. The paper proposes an…

AdaPT：利用辅助信息的交互式多重检验程序AI 解读

Summary We consider the problem of multiple-hypothesis testing with generic side information: for each hypothesis Hi we observe both a p-value pi and some predictor xi encoding contextual information about the hypothesis. For large-scale problems, adaptively focusing power on the more promising hypotheses (those more likely to yield discoveries) can lead to much more powerful multiple-testing procedures. We propose a general iterative framework for this problem, the adaptive…

超越可分解图的高斯图模型贝叶斯推断AI 解读

Summary Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that, when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general non-decomposable setting. Penalized likelihood inference in contrast has made tremendous gains in the past few years in terms of scalability and tractability. Bayesian inference, however, has not had the same level of success, though a…