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TENET：尾部事件驱动的网络风险AI 解读

CoVaR is a measure for systemic risk of the networked financial system conditional on institutions being under distress. The analysis of systemic risk is the focus of recent econometric analyses and uses tail event and network based techniques. Here, in this paper we bring tail event and network dynamics together into one context. In order to pursue such joint efforts, we propose a semiparametric measure to estimate systemic interconnectedness across financial institutions…

基于分位数的分类器AI 解读

Classification with small samples of high-dimensional data is important in many application areas. Quantile classifiers are distance-based classifiers that require a single parameter, regardless of the dimension, and classify observations according to a sum of weighted componentwise distances of the components of an observation to the within-class quantiles. An optimal percentage for the quantiles can be chosen by minimizing the misclassification error in the training…

凸性约束下非参数工具变量回归的不适定性AI 解读

This note shows that adding monotonicity or convexity constraints on the regression function does not restore well‐posedness in nonparametric instrumental variable regression. The minimum distance problem without regularization is still locally ill‐posed.

高维近似因子模型的最大似然估计与推断AI 解读

An approximate factor model of high dimension has two key features. First, the idiosyncratic errors are correlated and heteroskedastic over both the cross-section and time dimensions; the correlations and heteroskedasticities are of unknown forms. Second, the number of variables is comparable or even greater than the sample size. Thus, a large number of parameters exist under a high-dimensional approximate factor model. Most widely used approaches to estimation are principal…

序贯回归程序的精确选择后推断AI 解读

We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to perform valid inference after any selection event that can be characterized as y falling into a polyhedral set. This framework allows us to derive conditional (post-selection) hypothesis tests at any step of forward stepwise or least angle regression, or any step along the lasso…

迹追踪：无模型变量选择的一般框架AI 解读

We propose trace pursuit for model-free variable selection under the sufficient dimension-reduction paradigm. Two distinct algorithms are proposed: stepwise trace pursuit and forward trace pursuit. Stepwise trace pursuit achieves selection consistency with fixed p. Forward trace pursuit can serve as an initial screening step to speed up the computation in the case of ultrahigh dimensionality. The screening consistency property of forward trace pursuit based on sliced inverse…

协方差矩阵的凸带状化估计AI 解读

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding…

基于多变量符号的高维两样本位置检验AI 解读

This article concerns tests for the two-sample location problem when data dimension is larger than the sample size. Existing multivariate-sign-based procedures are not robust against high dimensionality, producing tests with Type I error rates far away from nominal levels. This is mainly due to the biases from estimating location parameters. We propose a novel test to overcome this issue by using the “leave-one-out” idea. The proposed test statistic is scalar-invariant and…

稳健正交补主成分分析AI 解读

Recently, the robustification of principal component analysis (PCA) has attracted lots of attention from statisticians, engineers, and computer scientists. In this work, we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal subspace estimation. Based on a mathematical formulation of such transformed outliers, a novel robust orthogonal complement principal component analysis (ROC-PCA) is…

变量数远超样本量时典型判别向量的同步稀疏估计AI 解读

This article considers the problem of sparse estimation of canonical vectors in linear discriminant analysis when p ≫ N. Several methods have been proposed in the literature that estimate one canonical vector in the two-group case. However, G − 1 canonical vectors can be considered if the number of groups is G. In the multi-group context, it is common to estimate canonical vectors in a sequential fashion. Moreover, separate prior estimation of the covariance structure is…

纳入预测变量图结构的稀疏回归AI 解读

With the abundance of high dimensional data in various disciplines, sparse regularized techniques are very popular these days. In this paper, we make use of the structure information among predictors to improve sparse regression models. Typically, such structure information can be modeled by the connectivity of an undirected graph using all predictors as nodes of the graph. Most existing methods use this undirected graph edge-by-edge to encourage the regression coefficients…

用于高维分类的贝叶斯条件张量分解AI 解读

In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors. In settings such as genomics, there can be complex interactions among the predictors. By using a carefully-structured Tucker factorization, we define a model that can characterize any conditional probability, while facilitating variable…

从现代优化视角求解最佳子集选择AI 解读

In the period 1991–2015, algorithmic advances in Mixed Integer Optimization (MIO) coupled with hardware improvements have resulted in an astonishing 450 billion factor speedup in solving MIO problems. We present a MIO approach for solving the classical best subset selection problem of choosing $k$ out of $p$ features in linear regression given $n$ observations. We develop a discrete extension of modern first-order continuous optimization methods to find high quality feasible…

利用 Kac–Rice 公式进行自适应回归推断AI 解读

We derive an exact $p$-value for testing a global null hypothesis in a general adaptive regression setting. Our approach uses the Kac–Rice formula [as described in Random Fields and Geometry (2007) Springer, New York] applied to the problem of maximizing a Gaussian process. The resulting test statistic has a known distribution in finite samples, assuming Gaussian errors. We examine this test statistic in the case of the lasso, group lasso, principal components and matrix…

基于 Pauli 测量的最优大规模量子态层析AI 解读

Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of high-dimensional density matrices based on Pauli measurements. In particular, under appropriate notion of sparsity, we establish the minimax optimal rates of convergence for estimation of the density matrix under both the spectral and Frobenius norm…

高维自协方差矩阵的大样本行为AI 解读

The existence of limiting spectral distribution (LSD) of $\hat{\Gamma}_{u}+\hat{\Gamma}_{u}^{*}$, the symmetric sum of the sample autocovariance matrix $\hat{\Gamma}_{u}$ of order $u$, is known when the observations are from an infinite dimensional vector linear process with appropriate (strong) assumptions on the coefficient matrices. Under significantly weaker conditions, we prove, in a unified way, that the LSD of any symmetric polynomial in these matrices such as $\hat{\Gamma}_{u}+\hat{\Gamma}_{u}^{*}$…

基于边际经验似然的非参数与半参数模型局部独立特征筛选AI 解读

We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the underlying data model, our approach accommodates a wide spectrum of nonparametric and semiparametric model families. To detect the local contributions of explanatory variables, our approach constructs empirical likelihood locally in…

贝叶斯流形回归AI 解读

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface based on limited data. Fortunately, in many applications, the support of the data is concentrated on a $d$-dimensional subspace with $d\ll D$. Manifold learning attempts to estimate this subspace. Our focus is on developing computationally…

稀疏精度矩阵估计：最优收敛率与自适应估计AI 解读

Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of convergence are established for a range of matrix norm losses. A fully data driven estimator based on adaptive constrained $\ell_{1}$ minimization is proposed and its rate of convergence is obtained over a collection of parameter spaces. The…

高维时间序列中多个图模型的联合估计AI 解读

Summary We consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a measure of closeness between subjects. We propose a kernel-based method for jointly estimating all graphical models. Theoretically, under a double asymptotic framework,…

时间序列经验似然方法的覆盖率上界问题AI 解读

Summary The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood and non-standard expansive empirical likelihood methods for time series data are investigated via studying the probability of violating the convex hull constraint. The large sample bounds are derived on the basis of the pivotal limit of the blockwise empirical log-likelihood ratio obtained under fixed b asymptotics, which has recently been shown to provide…

非高斯与异方差误差下高维时间序列模型的ℓ₁正则化AI 解读

We study the asymptotic properties of the Adaptive LASSO (adaLASSO) in sparse, high-dimensional, linear time-series models. The adaLASSO is a one-step implementation of the family of folded concave penalized least-squares. We assume that both the number of covariates in the model and the number of candidate variables can increase with the sample size (polynomially or geometrically). In other words, we let the number of candidate variables to be larger than the number of…

通过自适应组融合LASSO估计面板共同突变AI 解读

In this paper we consider estimation and inference of common breaks in panel data models via adaptive group fused Lasso. We consider two approaches—penalized least squares (PLS) for first-differenced models without endogenous regressors, and penalized GMM (PGMM) for first-differenced models with endogeneity. We show that with probability tending to one, both methods can correctly determine the unknown number of breaks and estimate the common break dates consistently. We…

通过惩罚最大似然高效估计近似因子模型AI 解读

We study an approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. For efficient estimations it is essential to estimate a large error covariance matrix. We estimate the common factors and factor loadings based on maximizing a Gaussian quasi-likelihood, through penalizing a large covariance sparse matrix. The weighted ℓ1 penalization is employed. While the principal components (PC) based methods estimate the covariance matrices…