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多面体约束条件下模型选择后置信区间的长度AI 解读

Valid inference after model selection is currently a very active area of research. The polyhedral method, pioneered by Lee, et al. (2016), allows for valid inference after model selection if the model selection event can be described by polyhedral constraints. In that reference, the method is exemplified by constructing two valid confidence intervals when the Lasso estimator is used to select a model. We here study the length of these intervals. For one of these confidence…

高维相关数据分析的分布式整合矩方法AI 解读

This paper is motivated by a regression analysis of electroencephalography (EEG) neuroimaging data with high-dimensional correlated responses with multi-level nested correlations. We develop a divide-and-conquer procedure implemented in a fully distributed and parallelized computational scheme for statistical estimation and inference of regression parameters. Despite significant efforts in the literature, the computational bottleneck associated with high-dimensional…

稀疏图中协变量正则化的社区发现AI 解读

In this article, we investigate community detection in networks in the presence of node covariates. In many instances, covariates and networks individually only give a partial view of the cluster structure. One needs to jointly infer the full cluster structure by considering both. In statistics, an emerging body of work has been focused on combining information from both the edges in the network and the node covariates to infer community memberships. However, so far the…

高维 Logistic 回归的全局与同时假设检验AI 解读

High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this paper, global testing and large-scale multiple testing for the regression coefficients are considered in both single- and two-regression settings. A test statistic for testing the global null hypothesis is constructed using a generalized low-dimensional projection for bias correction and its asymptotic null distribution is derived. A lower bound for the global testing is…

基于 Copula 的聚类数据随机效应模型AI 解读

In a binary choice panel data framework, probabilities of the outcomes of several individuals depend on the correlation of the unobserved heterogeneity. I propose a random effects estimator that models the correlation of the unobserved heterogeneity among individuals in the same cluster using a copula. I discuss the asymptotic efficiency of the estimator relative to standard random effects estimators, and to choose the copula I propose a specification test. The…

用逐节点回归估计高维投资组合AI 解读

This article investigates the large sample properties of the variance, weights, and risk of high-dimensional portfolios where the inverse of the covariance matrix of excess asset returns is estimated using a technique called nodewise regression. Nodewise regression provides a direct estimator for the inverse covariance matrix using the least absolute shrinkage and selection operator to estimate the entries of a sparse precision matrix. We show that the variance, weights, and…

利用消息传递算法进行高维宏观经济预测AI 解读

This article proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility, and exogenous predictors, as an equivalent high-dimensional static regression problem with thousands of covariates. Inference in this specification proceeds using Bayesian hierarchical priors that shrink the high-dimensional vector of coefficients either…

通过模型复杂度选择估计主流形AI 解读

Abstract We propose a framework of principal manifolds to model high-dimensional data. This framework is based on Sobolev spaces and designed to model data of any intrinsic dimension. It includes principal component analysis and principal curve algorithm as special cases. We propose a novel method for model complexity selection to avoid overfitting, eliminate the effects of outliers and improve the computation speed. Additionally, we propose a method for identifying the…

复杂区域上的非参数密度估计AI 解读

Abstract We propose a nonparametric method for density estimation over (possibly complicated) spatial domains. The method combines a likelihood approach with a regularization based on a differential operator. We demonstrate the good inferential properties of the method. Moreover, we develop an estimation procedure based on advanced numerical techniques, and in particular making use of finite elements. This ensures high computational efficiency and enables great flexibility.…

利用迭代 α 扩展从线性测量中估计梯度稀疏信号AI 解读

Abstract We consider estimating a piecewise-constant image, or a gradient-sparse signal on a general graph, from noisy linear measurements. We propose and study an iterative algorithm to minimize a penalized least-squares objective, with a penalty given by the “ℓ0-norm” of the signal’s discrete graph gradient. The method uses a non-convex variant of proximal gradient descent, applying the alpha-expansion procedure to approximate the proximal mapping in each iteration, and…

高维均值向量变点的有限样本推断与定位AI 解读

Abstract Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a Gaussian multiplier bootstrap to calibrate critical values of the CUSUM test statistics in high dimensions. The proposed bootstrap CUSUM test is fully data dependent and it has strong theoretical guarantees under arbitrary dependence…

高维 LASSO 变量选择一致性的充要条件AI 解读

This paper investigates conditions for variable selection consistency of the LASSO in high dimensional regression models and gives necessary and sufficient conditions for the same, potentially allowing the model dimension p to grow arbitrarily fast as a function of the sample size n. These conditions require both upper and lower bounds on the growth rate of the penalty parameter. It turns out that a variant of the irrepresentable Condition (IRC) of (J. Mach. Learn. Res. 7…

光滑最优传输映射的极小极大估计AI 解读

Brenier’s theorem is a cornerstone of optimal transport that guarantees the existence of an optimal transport map T between two probability distributions P and Q over Rd under certain regularity conditions. The main goal of this work is to establish the minimax estimation rates for such a transport map from data sampled from P and Q under additional smoothness assumptions on T. To achieve this goal, we develop an estimator based on the minimization of an empirical version of…

高维与非欧几里得数据的多尺度几何特征提取及应用AI 解读

A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. Based on geometric considerations, we map each pair of data points into a real-valued feature function defined on the unit interval. Further statistical analysis is then based on the collection of feature functions. The potential of the method is illustrated by different applications, including classification and anomaly detection. Connections to other concepts, such as random…

利用对称性与形状约束的高维非参数密度估计AI 解读

We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on Rp and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and can mitigate the curse of dimensionality. Our main symmetry assumption is that the super-level sets of the density are K-homothetic (i.e., scalar multiples of a convex body K⊆Rp). When K is known, we prove that the K-homothetic log-concave maximum…

稀疏高维变点检测的极小极大速率AI 解读

We study the detection of a sparse change in a high-dimensional mean vector as a minimax testing problem. Our first main contribution is to derive the exact minimax testing rate across all parameter regimes for n independent, p-variate Gaussian observations. This rate exhibits a phase transition when the sparsity level is of order ploglog(8n) and has a very delicate dependence on the sample size: in a certain sparsity regime, it involves a triple iterated logarithmic factor…

概率测度间熵正则最优传输随机算法的渐近分布与收敛速率AI 解读

This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal transportation problems can be rewritten as a nonstrongly concave optimisation problem. It allows to implement a Robbins–Monro stochastic algorithm to estimate the Sinkhorn divergence using a sequence of data sampled from one of the two distributions.…

高维协变量观察性研究中的重叠性AI 解读

Estimating causal effects under exogeneity hinges on two key assumptions: unconfoundedness and overlap. Researchers often argue that unconfoundedness is more plausible when more covariates are included in the analysis. Less discussed is the fact that covariate overlap is more difficult to satisfy in this setting. In this paper, we explore the implications of overlap in observational studies with high-dimensional covariates and formalize curse-of-dimensionality argument,…

椭圆分布及其推广下的高维协方差矩阵检验AI 解读

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem for linear spectral statistics of the sample covariance matrix based on self-normalized observations. For testing sphericity, our tests neither assume specific parametric distributions nor involve the kurtosis of data. More generally, we can test against any non-negative definite matrix that can even be not invertible. As an…

大维动态因子模型：含一阶单整协整因子的脉冲响应估计AI 解读

We study a large-dimensional Dynamic Factor Model where: (i) the vector of factors Ft is I(1) and driven by a number of shocks that is smaller than the dimension of Ft; and, (ii) the idiosyncratic components are either I(1) or I(0). Under (i), the factors Ft are cointegrated and can be modeled as a Vector Error Correction Model (VECM). Under (i) and (ii), we provide consistent estimators, as both the cross-sectional size n and the time dimension T go to infinity, for the…

非参数部分识别下部分线性工具变量模型的稳健与最优估计AI 解读

This paper studies robust and optimal estimation of the slope coefficients in a partially linear instrumental variables model with nonparametric partial identification. We establish the root-n asymptotic normality of a penalized sieve minimum distance estimator of the slope coefficients. We show that the asymptotic normality holds regardless of whether the nonparametric function is point identified or only partially identified. However, in the presence of nonparametric…

共轭向量自回归模型中收缩与稀疏性的结合AI 解读

Summary Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models. But at the same time, they introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a straightforward means of postprocessing posterior estimates of a conjugate Bayesian VAR to effectively perform equation‐specific covariate selection. Compared with existing techniques using shrinkage alone, our approach combines…

具有网络结构的高维协方差矩阵的模型平均估计AI 解读

Summary In this paper, we develop a model averaging method to estimate a high-dimensional covariance matrix, where the candidate models are constructed by different orders of polynomial functions. We propose a Mallows-type model averaging criterion and select the weights by minimizing this criterion, which is an unbiased estimator of the expected in-sample squared error plus a constant. Then, we prove the asymptotic optimality of the resulting model average covariance…

异质性因果效应的机器学习估计：经验蒙特卡洛证据AI 解读

Summary We investigate the finite-sample performance of causal machine learning estimators for heterogeneous causal effects at different aggregation levels. We employ an empirical Monte Carlo study that relies on arguably realistic data generation processes (DGPs) based on actual data in an observational setting. We consider 24 DGPs, eleven causal machine learning estimators, and three aggregation levels of the estimated effects. Four of the considered estimators perform…