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利用惩罚样条估计含非平稳解释变量的变系数模型AI 解读

This paper considers estimation and inference for varying-coefficient models with nonstationary regressors. We propose a nonparametric estimation method using penalized splines, which achieves the same optimal convergence rate as kernel-based methods, but enjoys computation advantages. Utilizing the mixed model representation of penalized splines, we develop a likelihood ratio test statistic for checking the stability of the regression coefficients. We derive both the exact…

高维地标式二维形状数据的聚类AI 解读

An important goal in image analysis is to cluster and recognize objects of interest according to the shapes of their boundaries. Clustering such objects faces at least four major challenges including a curved shape space, a high-dimensional feature space, a complex spatial correlation structure, and shape variation associated with some covariates (e.g., age or gender). The aim of this article is to develop a penalized model-based clustering framework to cluster…

高维高斯图模型中用于网络构建的等价偏相关度量AI 解读

Gaussian graphical models (GGMs) are frequently used to explore networks, such as gene regulatory networks, among a set of variables. Under the classical theory of GGMs, the construction of Gaussian graphical networks amounts to finding the pairs of variables with nonzero partial correlation coefficients. However, this is infeasible for high-dimensional problems for which the number of variables is larger than the sample size. In this article, we propose a new measure of…

大量相关正态变量的经验分布AI 解读

Motivated by the advent of high dimensional highly correlated data, this work studies the limit behavior of the empirical cumulative distribution function (ecdf) of standard normal random variables under arbitrary correlation. First, we provide a necessary and sufficient condition for convergence of the ecdf to the standard normal distribution. Next, under general correlation, we show that the ecdf limit is a random, possible infinite, mixture of normal distribution…

高维协方差矩阵估计的带宽选择AI 解读

Yumou Qiu & Song Xi ChenYumou Qiu is Assistant Professor, Department of Statistics, University of Nebraska-Lincoln, NE 68583-0963 (E-mail: ). Song Xi Chen is Chair Professor, Department of Business Statistics and Econometrics, Guanghua School of Management and Center for Statistical Science, Peking University, Beijing 100651, China, and Professor, Department of Statistics, Iowa State University, Ames, IA 50011-1210 (E-mail: ).We thank the editors, the AE and three anonymous…

基于偏微分方程惩罚空间回归的血流速度场估计AI 解读

We propose an innovative method for the accurate estimation of surfaces and spatial fields when prior knowledge of the phenomenon under study is available. The prior knowledge included in the model derives from physics, physiology, or mechanics of the problem at hand, and is formalized in terms of a partial differential equation governing the phenomenon behavior, as well as conditions that the phenomenon has to satisfy at the boundary of the problem domain. The proposed…

函数型主成分分析的 S 估计量AI 解读

Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this article, we propose a new class of estimators for principal components based on robust scale estimators. For a fixed dimension q, we robustly estimate the q-dimensional linear space that…

混合广义经验似然估计：使用自适应Lasso选择工具变量AI 解读

In this paper, we use the adaptive lasso estimator to choose the relevant instruments and eliminate the irrelevant instruments. The limit theory of Zou (2006) is extended from univariate iid case to heteroskedastic and non Gaussian data. Then we use the selected instruments in generalized empirical likelihood estimators (GEL). In this sense, these are called hybrid GEL. It is also shown that the lasso estimators are not model selection consistent whereas the adaptive lasso…

时变参数回归模型的半参数建模AI 解读

This paper considers the problem of semiparametric model building for linear regression models with potentially time-varying coefficients. By allowing the response variable and explanatory variables be jointly a nonstationary process, the proposed methods are widely applicable to nonstationary and dependent observations. We propose a local linear shrinkage method that can simultaneously achieve parameter estimation and variable selection. Its selection consistency and the…

半正定松弛能否将稀疏主成分分析推进至信息极限？AI 解读

Estimating the leading principal components of data, assuming they are sparse, is a central task in modern high-dimensional statistics. Many algorithms were developed for this sparse PCA problem, from simple diagonal thresholding to sophisticated semidefinite programming (SDP) methods. A key theoretical question is under what conditions can such algorithms recover the sparse principal components? We study this question for a single-spike model with an $\ell_{0}$-sparse…

稀疏高维变系数模型的非渐近极小极大研究AI 解读

The objective of the present paper is to develop a minimax theory for the varying coefficient model in a nonasymptotic setting. We consider a high-dimensional sparse varying coefficient model where only few of the covariates are present and only some of those covariates are time dependent. Our analysis allows the time-dependent covariates to have different degrees of smoothness and to be spatially inhomogeneous. We develop the minimax lower bounds for the quadratic risk and…

高维非线性分类的创新变换交互项筛选AI 解读

This paper is concerned with the problems of interaction screening and nonlinear classification in a high-dimensional setting. We propose a two-step procedure, IIS-SQDA, where in the first step an innovated interaction screening (IIS) approach based on transforming the original $p$-dimensional feature vector is proposed, and in the second step a sparse quadratic discriminant analysis (SQDA) is proposed for further selecting important interactions and main effects and…

维度可能增长的多元时间序列协方差估计与线性过程自助法AI 解读

Multivariate time series present many challenges, especially when they are high dimensional. The paper’s focus is twofold. First, we address the subject of consistently estimating the autocovariance sequence; this is a sequence of matrices that we conveniently stack into one huge matrix. We are then able to show consistency of an estimator based on the so-called flat-top tapers; most importantly, the consistency holds true even when the time series dimension is allowed to…

经济理论与预测：来自文献的经验AI 解读

Does economic theory help in forecasting key macroeconomic variables? This article aims to provide some insight into the question by drawing lessons from the literature. The definition of ‘economic theory’ includes a broad range of examples, such as accounting identities, disaggregation and spatial restrictions when forecasting aggregate variables, cointegration and forecasting with dynamic stochastic general equilibrium (DSGE) models. We group the lessons into three themes.…

选择有效且相关的矩条件：多矩GMM的信息型LASSOAI 解读

This paper studies the selection of valid and relevant moments for the generalized method of moments (GMM) estimation. For applications with many candidate moments, our asymptotic analysis accommodates a diverging number of moments as the sample size increases. The proposed procedure achieves three objectives in one-step: (i) the valid and relevant moments are distinguished from the invalid or irrelevant ones; (ii) all desired moments are selected in one step instead of in a…

多工具变量下的正则化有限信息最大似然估计AI 解读

The use of many moment conditions improves the asymptotic efficiency of the instrumental variables estimators. However, in finite samples, the inclusion of an excessive number of moments increases the bias. To solve this problem, we propose regularized versions of the limited information maximum likelihood (LIML) based on three different regularizations: Tikhonov, Landweber–Fridman, and principal components. Our estimators are consistent and asymptotically normal under…

函数型线性模型中的工具变量估计AI 解读

In an increasing number of empirical studies, the dimensionality measured e.g. as the size of the parameter space of interest, can be very large. Two instances of large dimensional models are the linear regression with a large number of covariates and the estimation of a regression function with many instrumental variables. An appropriate setting to analyze high dimensional problems is provided by a functional linear model, in which the covariates belong to Hilbert spaces.…

高维向量自回归的 oracle 不等式AI 解读

This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample size. We also state conditions under which no relevant variables are excluded.

高维 ALASSO 残差经验过程及其函数型 oracle 性质AI 解读

This paper considers post variable-selection inference in a high dimensional penalized regression model based on the ALASSO method of Zou (2006). It is shown that under suitable sparsity conditions, the residual empirical process based on the ALASSO provides valid inference methodology in very high dimensional regression problems where conventional methods fail. It is also shown that the ALASSO based residual empirical process satisfies a functional oracle property, i.e., in…

稀疏函数型数据的有效降维AI 解读

We propose a method of effective dimension reduction for functional data, emphasizing the sparse design where one observes only a few noisy and irregular measurements for some or all of the subjects. The proposed method borrows strength across the entire sample and provides a way to characterize the effective dimension reduction space, via functional cumulative slicing. Our theoretical study reveals a bias-variance trade-off associated with the regularizing truncation and…

加性模型的自动结构恢复AI 解读

We propose an automatic structure recovery method for additive models, based on a backfitting algorithm coupled with local polynomial smoothing, in conjunction with a new kernel-based variable selection strategy. Our method produces estimates of the set of noise predictors, the sets of predictors that contribute polynomially at different degrees up to a specified degree M, and the set of predictors that contribute beyond polynomially of degree M. We prove consistency of the…

差异网络检验及其在基因交互识别中的应用AI 解读

Model organisms and human studies have yielded increasing empirical evidence that interactions among genes contribute broadly to genetic variation of complex traits. In the presence of gene-gene interactions, the dimensionality of the feature space becomes extremely high relative to the sample size. This poses a significant methodological challenge in the identification of gene-gene interactions. In this paper, by using a Gaussian graphical model framework, we translate the…

多元回归降秩估计量的有效自由度AI 解读

We study the effective degrees of freedom of a general class of reduced-rank estimators for multivariate regression in the framework of Stein's unbiased risk estimation. A finite-sample exact unbiased estimator is derived that admits a closed-form expression in terms of the thresholded singular values of the least-squares solution and hence is readily computable. The results continue to hold in the high-dimensional setting where both the predictor and the response dimensions…

Factor models have been applied extensively for forecasting when high-dimensional datasets are available. In this case, the number of variables can be very large. For instance, usual dynamic factor models in central banks handle over 100 variables. However, there is a growing body of literature indicating that more variables do not necessarily lead to estimated factors with lower uncertainty or better forecasting results. This paper investigates the usefulness of partial…