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含共同因子的高维向量自回归模型AI 解读

This paper studies high-dimensional vector autoregressions (VARs) augmented with common factors that allow for strong cross-sectional dependence. Models of this type provide a convenient mechanism for accommodating the interconnectedness and temporal co-variability that are often present in large dimensional systems. We propose an ℓ1-nuclear-norm regularized estimator and derive the non-asymptotic upper bounds for the estimation errors as well as large sample asymptotics for…

大型因子模型多重结构突变的组融合 LASSO 方法AI 解读

This paper reformulates the identification of multiple structural breaks in factor loadings as a problem of detecting structural breaks in a factor regression, where the estimated pseudo factor corresponding to the largest eigenvalue is regressed on the remaining estimated factors. As a result, a group fused Lasso based estimation procedure is proposed to identify the break dates. Our procedure is practically easy-to-implement with standard statistical packages, overcoming…

因子结构误差下网络溢出效应的收缩估计AI 解读

This paper explores the estimation of a panel data model with cross-sectional interaction that is flexible both in its approach to specifying the network of connections between cross-sectional units, and in controlling for unobserved heterogeneity. It is assumed that there are different sources of information available on a network, which can be represented in the form of multiple weights matrices. These matrices may reflect observed links, different measures of…

高维回归中的推断AI 解读

Abstract This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter, the remaining coefficients being nuisance parameters, and seeks an optimal interest-respecting transformation, inducing sparsity on the relevant blocks of the notional Fisher information matrix. The induced sparsity is exploited…

高维响应多元回归的响应变量最优子集选择AI 解读

Summary This article investigates the statistical problem of response-variable selection with high-dimensional response variables and a diverging number of predictor variables with respect to the sample size in the framework of multivariate linear regression. A response best-subset selection model is proposed by introducing a 0-1 selection indicator for each response variable, and then a response best-subset selector is developed by introducing a separation parameter and a…

高维高斯图模型的统一推断AI 解读

Summary Graphical models have become a popular tool for representing dependencies within large sets of variables and are crucial for representing causal structures. We provide results for uniform inference on high-dimensional graphical models, in which the number of target parameters $d$ is potentially much larger than the sample size, under approximate sparsity. Our results highlight how graphical models can be estimated and recovered using modern machine learning methods…

用于识别共同极端事件群组的球面聚类AI 解读

Summary There is growing empirical evidence that spherical $k$-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results supporting this approach, but also demonstrate some pitfalls. Furthermore, we show that an alternative cost function may be more appropriate for identifying concomitant extremes, and it results in a novel spherical $k$-principal-component…

变量选择、单调似然比与组稀疏性AI 解读

In the pivotal variable selection problem, we derive the exact nonasymptotic minimax selector over the class of all s-sparse vectors, which is also the Bayes selector with respect to the uniform prior. While this optimal selector is, in general, not realizable in polynomial time, we show that its tractable counterpart (the scan selector) attains the minimax expected Hamming risk to within factor 2, and is also exact minimax with respect to the probability of wrong recovery.…

含测量误差的高维泊松模型：非线性非凸优化中的假设检验AI 解读

We study estimation and testing in the Poisson regression model with noisy high-dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a nonconvex target function to minimize. Treating the high-dimensional issue further leads us to augment an amenable penalty term to the target function. We propose to estimate the regression parameter through minimizing the penalized target…

高维潜在面板分位数回归及其资产定价应用AI 解读

We propose a generalization of the linear panel quantile regression model to accommodate both sparse and dense parts: sparse means that while the number of covariates available is large, potentially only a much smaller number of them have a nonzero impact on each conditional quantile of the response variable; while the dense part is represent by a low-rank matrix that can be approximated by latent factors and their loadings. Such a structure poses problems for traditional…

刻画 SLOPE 的权衡：变分视角与 Donoho–Tanner 极限AI 解读

Sorted ℓ1 regularization has been incorporated into many methods for solving high-dimensional statistical estimation problems, including the SLOPE estimator in linear regression. In this paper, we study how this relatively new regularization technique improves variable selection by characterizing the optimal SLOPE trade-off between the false discovery proportion (FDP) and true positive proportion (TPP) or, equivalently, between measures of type I error and power. Assuming a…

基于离散优化的分组变量选择：计算与统计视角AI 解读

We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on optimal solutions for the ℓ0-regularized formulation, a problem that is relatively unexplored due to computational challenges. Our methodology covers both high-dimensional linear regression and nonparametric sparse additive modeling with…

高维半参数矩约束模型AI 解读

We consider nonlinear moment restriction semiparametric models where both the dimension of the parameter vector and the number of restrictions are divergent with sample size and an unknown smooth function is involved. We propose an estimation method based on the sieve generalized method of moments (sieve-GMM). We establish consistency and asymptotic normality for the estimated quantities when the number of parameters increases modestly with sample size. We also consider the…

拓展正则化网络：多维正则化AI 解读

This paper derives asymptotic risk (expected loss) results for shrinkage estimators with multidimensional regularization in high-dimensional settings. We introduce a class of multidimensional shrinkage estimators (MuSEs), which includes the elastic net, and show that—as the number of parameters to estimate grows—the empirical loss converges to the oracle-optimal risk. This result holds when the regularization parameters are estimated empirically via cross-validation or…

纵向数据的超高维分位数回归：血压分析应用AI 解读

Despite major advances in research and treatment, identifying important genotype risk factors for high blood pressure remains challenging. Traditional genome-wide association studies (GWAS) focus on one single nucleotide polymorphism (SNP) at a time. We aim to select among over half a million SNPs along with time-varying phenotype variables via simultaneous modeling and variable selection, focusing on the most dangerous blood pressure levels at high quantiles. Taking…

利用函数型预测变量的贝叶斯空间变系数模型预测作物产量AI 解读

Reliable prediction for crop yield is crucial for economic planning, food security monitoring, and agricultural risk management. This study aims to develop a crop yield forecasting model at large spatial scales using meteorological variables closely related to crop growth. The influence of climate patterns on agricultural productivity can be spatially inhomogeneous due to local soil and environmental conditions. We propose a Bayesian spatially varying functional model…

用于正则化非线性回归的随机树集成AI 解读

This article develops a novel stochastic tree ensemble method for nonlinear regression, referred to as accelerated Bayesian additive regression trees, or XBART. By combining regularization and stochastic search strategies from Bayesian modeling with computationally efficient techniques from recursive partitioning algorithms, XBART attains state-of-the-art performance at prediction and function estimation. Simulation studies demonstrate that XBART provides accurate point-wise…

高维混杂下加性风险模型的治疗效应估计AI 解读

Estimating treatment effects for survival outcomes in the high-dimensional setting is critical for many biomedical applications and any application with censored observations. This article establishes an “orthogonal” score for learning treatment effects, using observational data with a potentially large number of confounders. The estimator allows for root-n, asymptotically valid confidence intervals, despite the bias induced by the regularization. Moreover, we develop a…

大规模向量自回归移动平均模型的稀疏识别与估计AI 解读

The Vector AutoRegressive Moving Average (VARMA) model is fundamental to the theory of multivariate time series; however, identifiability issues have led practitioners to abandon it in favor of the simpler but more restrictive Vector AutoRegressive (VAR) model. We narrow this gap with a new optimization-based approach to VARMA identification built upon the principle of parsimony. Among all equivalent data-generating models, we use convex optimization to seek the…

通过 Thompson 抽样进行变量选择AI 解读

–Thompson sampling is a heuristic algorithm for the multi-armed bandit problem which has a long tradition in machine learning. The algorithm has a Bayesian spirit in the sense that it selects arms based on posterior samples of reward probabilities of each arm. By forging a connection between combinatorial binary bandits and spike-and-slab variable selection, we propose a stochastic optimization approach to subset selection called Thompson variable selection (TVS). TVS is a…

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…

通过剖面化与袋装法估计稀疏时空自回归模型AI 解读

We consider a new class of spatio-temporal models with sparse autoregressive coefficient matrices and exogenous variable. To estimate the model, we first profile the exogenous variable out of the response. This leads to a profiled model structure. Next, to overcome endogeneity issue, we propose a class of generalized methods of moment (GMM) estimators to estimate the autoregressive coefficient matrices. A novel bagging-based estimator is further developed to conquer the…

高维关联度表估计：从部门溢出理解大缓和AI 解读

We estimate sectoral spillovers around the Great Moderation with the help of forecast error variance decomposition tables. Obtaining such tables in high dimensions is challenging because they are functions of the estimated vector autoregressive coefficients and the residual covariance matrix. In a simulation study, we compare various regularization methods on both and conduct a comprehensive analysis of their performance. We show that standard estimators of large…

弱依赖高维动态面板中的异质性处理效应推断AI 解读

This paper provides estimation and inference methods for conditional average treatment effects (CATE) characterized by a high‐dimensional parameter in both homogeneous cross‐sectional and unit‐heterogeneous dynamic panel data settings. In our leading example, we model CATE by interacting the base treatment variable with explanatory variables. The first step of our procedure is orthogonalization, where we partial out the controls and unit effects from the outcome and the base…