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高维典型相关分析的显著性检验AI 解读

Summary We consider the problem of testing for the presence of linear relationships between large sets of random variables based on a postselection inference approach to canonical correlation analysis. The challenge is to adjust for the selection of subsets of variables having linear combinations with maximal sample correlation. To this end, we construct a stabilized one-step estimator of the Euclidean norm of the canonical correlations maximized over subsets of variables of…

关于《多元依赖的多尺度 Fisher 独立性检验》的讨论AI 解读

We read with interest the work of Gorsky & Ma (2022) on statistical dependence testing using a multi-scale Fisher’s independence test, MultiFIT. The procedure consists of first transforming the data to map to the unit ball, then performing univariate Fisher’s exact tests of independence on a collection of |$2 \times 2$| contingency tables, and finally correcting for the use of multiple testing. The collection is obtained using a divide-and-conquer approach with a…

关于“多元依赖的多尺度 Fisher 独立性检验”的讨论：二进制展开视角AI 解读

The multi-scale Fisher’s independence test, MultiFIT, proposed by Gorsky & Ma (2022) is a novel method to test independence between two random vectors. By its design, this test is particularly useful in detecting local dependence. Moreover, by adopting a resampling-free approach, it can easily accommodate massive sample sizes. Another benefit of the proposed method is its ability to interpret the nature of dependency. We congratulate the authors for their very interesting…

关于“多元依赖的多尺度 Fisher 独立性检验”的讨论：文献定位与选择标准AI 解读

We would like to congratulate the authors on an interesting paper that provides many avenues for discussion. The reduction of a nonparametric problem to a sequence of |$2 \times 2$| contingency tables is very elegant, and Fisher’s exact test is used to great effect. There are now a large number of methods for multivariate independence testing, but the proposed procedure stands out by providing uniform Type I error controls without a large computational burden, combining the…

多元依赖的多尺度 Fisher 独立性检验AI 解读

Summary Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample size, making it difficult to apply them in the presence of massive sample sizes. Moreover, resampling is usually necessary to evaluate the statistical significance of the resulting test statistics at finite sample sizes, further…

结合高维节点变量的网络联合潜在空间模型AI 解读

Summary Network latent space models assume that each node is associated with an unobserved latent position in a Euclidean , and such latent variables determine the probability of two nodes connecting with each other. In many applications, nodes in the network are often observed along with high-dimensional node variables, and these node variables provide important information for understanding the network structure. However, classical network latent space models have several…

异质系数、控制变量与多重处理效应识别AI 解读

Summary Multi-dimensional heterogeneity and endogeneity are important features of models with multiple treatments. We consider a heterogeneous coefficients model where the outcome is a linear combination of dummy treatment variables, with each variable representing a different kind of treatment. We use control variables to give necessary and sufficient conditions for identification of average treatment effects. With mutually exclusive treatments we find that, provided the…

利用协变量的局部线性graphon估计AI 解读

Summary We consider local linear estimation of the graphon function, which determines probabilities of pairwise edges between nodes in an unlabelled network. Real-world networks are typically characterized by node heterogeneity, with different nodes exhibiting different degrees of interaction. Existing approaches to graphon estimation are limited to local constant approximations, and are not designed to estimate heterogeneity across the full network. In this paper, we show…

具有共享结构的多层网络潜在空间模型AI 解读

Summary Latent space models are frequently used for modelling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well developed for more complex network structures, which are becoming increasingly common in practice. In this article we propose a new latent space model for multiplex networks, i.e., multiple heterogeneous networks observed on a shared node set. Multiplex…

利用多环境knockoff筛选寻找稳健关联AI 解读

Summary In this article we develop a method based on model-X knockoffs to find conditional associations that are consistent across environments, while controlling the false discovery rate. The motivation for this problem is that large datasets may contain numerous associations that are statistically significant and yet misleading, as they are induced by confounders or sampling imperfections. However, associations replicated under different conditions may be more interesting.…

多元点过程的小波谱AI 解读

Summary Wavelets provide the flexibility for analysing stochastic processes at different scales. In this article we apply them to multivariate point processes as a means of detecting and analysing unknown nonstationarity, both within and across component processes. To provide statistical tractability, a temporally smoothed wavelet periodogram is developed and shown to be equivalent to a multi-wavelet periodogram. Under a stationarity assumption, the distribution of the…

条件随机化检验与knockoff的高维功效分析AI 解读

Summary In many scientific applications, researchers aim to relate a response variable $Y$ to a set of potential explanatory variables $X = (X_1,\dots,X_p)$, and start by trying to identify variables that contribute to this relationship. In statistical terms, this goal can be understood as trying to identify those $X_j$ on which $Y$ is conditionally dependent. Sometimes it is of value to simultaneously test for each $j$, which is more commonly known as variable selection.…

存在不依从时意向治疗Wilcoxon–Mann–Whitney检验的相对效率AI 解读

Summary A general framework is set up to study the asymptotic properties of the intent-to-treat Wilcoxon–Mann–Whitney test in randomized experiments with nonignorable noncompliance. Under location-shift alternatives, the Pitman efficiencies of the intent-to-treat Wilcoxon–Mann–Whitney and $t$ tests are derived. It is shown that the former is superior if the compliers are more likely to be found in high-density regions of the outcome distribution or, equivalently, if the…

析因实验中的回归因果推断：目标量、模型设定与基于设计的性质AI 解读

Summary Factorial designs are widely used because of their ability to accommodate multiple factors simultaneously. Factor-based regression with main effects and some interactions is the dominant strategy for downstream analysis, delivering point estimators and standard errors simultaneously via one least-squares fit. Justification of these convenient estimators from the design-based perspective requires quantifying their sampling properties under the assignment mechanism…

用于估计时间平均协方差矩阵的翼帆型滞后窗AI 解读

Summary Lag windows are commonly used in time series analysis, econometrics, steady-state simulation and Markov chain Monte Carlo to estimate time-average covariance matrices. In the presence of positive correlation in the underlying process, estimators of this matrix almost always exhibit significant negative bias, leading to undesirable finite-sample properties. We propose a new family of lag windows specifically designed to improve finite-sample performance by offsetting…

含重复观测数据的渐近分布无关变点检测AI 解读

Summary A nonparametric framework for changepoint detection, based on scan statistics utilizing graphs that represent similarities among observations, is gaining attention owing to its flexibility and good performance for high-dimensional and non-Euclidean data sequences. However, this graph-based framework faces challenges when there are repeated observations in the sequence, which is often the case for discrete data such as network data. In this article we extend the…

概率预测表现的有效序贯推断AI 解读

Summary Probability forecasts for binary events play a central role in many applications. Their quality is commonly assessed with proper scoring rules, which assign forecasts numerical scores such that a correct forecast achieves a minimal expected score. In this paper, we construct e-values for testing the statistical significance of score differences of competing forecasts in sequential settings. E-values have been proposed as an alternative to $p$-values for hypothesis…

分位数趋势滤波的风险界AI 解读

Summary We study quantile trend filtering, a recently proposed method for nonparametric quantile regression, with the goal of generalizing existing risk bounds for the usual trend-filtering estimators that perform mean regression. We study both the penalized and the constrained versions, of order $r \geqslant 1$, of univariate quantile trend filtering. Our results show that both the constrained and the penalized versions of order $r \geqslant 1$ attain the minimax rate up to…

高维广义潜因子模型中的因子数确定AI 解读

Summary As a generalization of the classical linear factor model, generalized latent factor models are useful for analysing multivariate data of different types, including binary choices and counts. This paper proposes an information criterion to determine the number of factors in generalized latent factor models. The consistency of the proposed information criterion is established under a high-dimensional setting, where both the sample size and the number of manifest…

广义极值分布最大似然估计的唯一性与全局最优性AI 解读

Summary The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory, and is in common use for analysing the far tail of observed phenomena, yet important asymptotic properties of likelihood-based estimation under this standard model have not been established. In this paper we prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit…

难处理后验的高效伯努利工厂马尔可夫链蒙特卡洛AI 解读

Summary Accept-reject-based Markov chain Monte Carlo algorithms have traditionally utilized acceptance probabilities that can be explicitly written as a function of the ratio of the target density at the two contested points. This feature is rendered almost useless in Bayesian posteriors with unknown functional forms. We introduce a new family of Markov chain Monte Carlo acceptance probabilities that has the distinguishing feature of not being a function of the ratio of the…

Chatterjee 秩相关的检验功效AI 解读

Summary Chatterjee (2021) introduced a simple new rank correlation coefficient that has attracted much attention recently. The coefficient has the unusual appeal that it not only estimates a population quantity first proposed by Dette et al. (2013) that is zero if and only if the underlying pair of random variables is independent, but also is asymptotically normal under independence. This paper compares Chatterjee’s new correlation coefficient with three established rank…

基于 Sard 方法的半精确控制泛函AI 解读

Summary A novel control variate technique is proposed for the post-processing of Markov chain Monte Carlo output, based on both Stein’s method and an approach to numerical integration due to Sard. The resulting estimators of posterior expected quantities of interest are proven to be polynomially exact in the Gaussian context, while empirical results suggest that the estimators approximate a Gaussian cubature method near the Bernstein–von Mises limit. The main theoretical…

高维半监督学习：寻求均值的最优推断AI 解读

Summary A fundamental challenge in semi-supervised learning lies in the observed data’s disproportional size when compared with the size of the data collected with missing outcomes. An implicit understanding is that the dataset with missing outcomes, being significantly larger, ought to improve estimation and inference. However, it is unclear to what extent this is correct. We illustrate one clear benefit: root-$n$ inference of the outcome’s mean is possible while only…