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分析随机特征与双层神经网络的对偶框架AI 解读

We consider the problem of learning functions within the Fp,π and Barron spaces, which play crucial roles in understanding random feature models (RFMs), two-layer neural networks as well as kernel methods. Leveraging tools from information-based complexity (IBC), we establish a dual equivalence between approximation and estimation and then apply it to study the learning of the preceding function spaces. The duality allows us to focus on the more tractable problem between…

一般函数空间中的最优传输映射估计AI 解读

We study the problem of estimating a function T, given independent samples from a distribution P and from the pushforward distribution T♯P. This setting is motivated by applications in the sciences, where T represents the evolution of a physical system over time, and in machine learning, where, for example, T may represent a transformation learned by a deep neural network trained for a generative modeling task. To ensure identifiability, we assume that T=∇φ0 is the gradient…

依赖结构下最大 Pearson 相关系数的渐近分布AI 解读

Given a random sample from a multivariate normal distribution whose covariance matrix is a Toeplitz matrix, we study the largest off-diagonal entry of the sample correlation matrix. Assuming the multivariate normal distribution has the covariance structure of an autoregressive sequence, we establish a phase transition in the limiting distribution of the largest off-diagonal entry. We show that the limiting distributions are of Gumbel-type (with different parameters),…

高斯序列模型中的稀疏性与相关性AI 解读

We study estimation of an s-sparse signal in the p-dimensional Gaussian sequence model with equicorrelated observations and derive the minimax rate. A new phenomenon emerges from correlation, namely, the rate scales with respect to p−2s and exhibits a phase transition at p−2s≍p. Correlation is shown to be a blessing, provided it is sufficiently strong and the critical correlation level exhibits a delicate dependence on the sparsity level. Due to correlation, the minimax rate…

维度增长下稀疏单指标模型的半参数估计与变量选择AI 解读

This paper considers semiparametric sieve estimation in high-dimensional single index models. The use of Hermite polynomials in approximating the unknown link function provides a convenient framework to conduct both estimation and variable selection. The estimation of the index parameter is formulated from solutions obtained by the routine penalized weighted linear regression procedure, where the weights are used in order to tackle the unbounded support of the regressors.…

交互固定效应下部分识别面板模型的推断AI 解读

In this paper, we develop methods for statistical inferences in a partially identified nonparametric panel data model with endogeneity and interactive fixed effects. Under some normalization rules, we can concentrate out the large-dimensional parameter vector of factor loadings and specify a set of conditional moment restrictions that are involved with only the finite-dimensional factor parameters along with the infinite-dimensional nonparametric component. For a conjectured…

面板数据模型中逐系数结构突变的估计AI 解读

When estimating structural breaks, existing econometric methods adopt an approach in which either all parameters change simultaneously, or they remain the same. In this paper, we consider the estimation of panel data models when an unknown subset of coefficients is subject to breaks. The challenge lies in estimating the breaks for each coefficient. To tackle this, we propose a new estimator for panel data, the “Coefficient-by-Coefficient Lasso” break estimator. This…

因子增广回归的分位数预测：结构不稳定性与模型不确定性AI 解读

The quantile regression is an effective tool in modeling data with heterogeneous conditional distribution. This paper considers the time-varying coefficient quantile predictive regression with factor-augmented predictors, to capture smooth structural changes and incorporate high-dimensional data information in prediction simultaneously. Uniform consistency of the local linear quantile coefficient estimators is established under misspecification. To further improve the…

高维线性时间序列的监督因子建模AI 解读

Motivated by Tucker tensor decomposition, this paper imposes low-rank structures to the column and row spaces of coefficient matrices in a multivariate infinite-order vector autoregression (VAR), which leads to a supervised factor model with two factor modelings being conducted to responses and predictors simultaneously. Interestingly, the stationarity condition implies an intrinsic weak group sparsity mechanism of infinite-order VAR, and hence a rank-constrained group Lasso…

高维因子模型的 Huber 主成分分析AI 解读

Factor models have been widely used in economics and finance. However, the heavy-tailed nature of macroeconomic and financial data is often neglected in statistical analysis. To address this issue, we propose a robust approach to estimate factor loadings and scores by minimizing the Huber loss function, which is motivated by the equivalence between conventional Principal Component Analysis (PCA) and the constrained least squares method in the factor model. We provide two…

稀疏高维加性模型的估计与一致推断AI 解读

We develop a novel method to construct uniformly valid confidence bands for a nonparametric component f1 in the sparse additive model Y=f1(X1)+…+fp(Xp)+ɛ in a high-dimensional setting. Our method integrates sieve estimation into a high-dimensional Z-estimation framework, facilitating the construction of uniformly valid confidence bands for the target component f1. To form these confidence bands, we employ a multiplier bootstrap procedure. Additionally, we provide rates for…

高维非线性模型基于自助法的渐近改进AI 解读

We consider penalized extremum estimation of a high-dimensional, possibly nonlinear model that is sparse in the sense that most of its parameters are zero but some are not. We use the SCAD penalty function, which provides model selection consistent and oracle efficient estimates under suitable conditions. However, asymptotic approximations based on the oracle model can be inaccurate with the sample sizes found in many applications. This paper gives conditions under which the…

当结构突变遇上门槛效应：结构不稳定下的因子分析AI 解读

Structural instability has been one of the central research questions in economics and finance over many decades. This paper systematically investigates structural instabilities in high dimensional factor models, which portray both structural breaks and threshold effects simultaneously. The observed high dimensional time series are concatenated at an unknown number of break points, while they are described by multiple threshold factor models that are heterogeneous between…

仿射模型中尖锐识别集的简易子向量推断AI 解读

This paper studies a regularized support function estimator for bounds on components of the parameter vector in the case in which the identified set is a polygon. The proposed regularized estimator has three important properties: (i) it has a uniform asymptotic Gaussian limit in the presence of flat faces in the absence of redundant (or overidentifying) constraints (or vice versa); (ii) the bias from regularization does not enter the first-order limiting distribution; (iii)…

有限混合模型的惩罚估计AI 解读

Economists often model unobserved heterogeneity using finite mixtures. In practice, the number of mixture components is rarely known. Model parameters lack point-identification if the estimation includes too many components, thus invalidating the classic properties of maximum likelihood estimation. I propose a penalized likelihood method to estimate finite mixtures with an unknown number of components. The resulting Order-Selection-Consistent Estimator (OSCE) consistently…

机器学习应助推谁：学生资助续申请实验中的因果与预测定向AI 解读

In many settings, interventions may be more effective for some individuals than for others, so that targeting interventions may be beneficial. We analyze the value of targeting in the context of a large-scale field experiment with over 53,000 college students, where the goal was to use “nudges” to encourage students to renew their financial-aid applications before a non-binding deadline. We begin with baseline approaches to targeting. First, we target based on a causal…

高维时间序列时变网络的估计AI 解读

We explore time-varying networks for high-dimensional locally stationary time series, using the large VAR model framework with both the transition and (error) precision matrices evolving smoothly over time. Two types of time-varying graphs are investigated: one containing directed edges of Granger causality linkages, and the other containing undirected edges of partial correlation linkages. Under the sparse structural assumption, we propose a penalised local linear method…

用卫星数据与神经网络追踪水泥生产AI 解读

This paper exploits daily infrared images taken from satellites to track economic activity in advanced and emerging countries. We first develop a framework to read, clean, and exploit satellite images. Our algorithm uses the laws of physics (Planck's law) and machine learning to detect the heat produced by cement plants in activity. This allows us to monitor in real-time whether a cement plant is working. Using this on around 1,000 plants, we construct a satellite-based…

流式数据平滑分位数回归的统计推断AI 解读

In this paper, we tackle the problem of conducting valid statistical inference for quantile regression with streaming data. The main difficulties are that the quantile regression loss function is non-smooth and it is often infeasible to store the entire dataset in memory, rendering traditional methodologies ineffective. We introduce a fully online updating method for statistical inference in smoothed quantile regression with streaming data to overcome these issues. Our main…

区间分位数相关及高维分位数效应检验AI 解读

In this article, we propose interval quantile correlation and interval quantile partial correlation to measure the association between two random variables over an interval of quantile levels. We construct efficient estimators for the proposed correlations, and establish their asymptotic properties under the null and alternative hypotheses. We further use the interval quantile partial correlation to test for the significance of covariate effects in high-dimensional quantile…

使用非线性筛方法推断时间序列非参数条件矩限制AI 解读

This paper studies estimation of and inference on dynamic nonparametric conditional moment restrictions of high dimensional variables for weakly dependent data, where the unknown functions of endogenous variables can be approximated via nonlinear sieves such as neural networks and Gaussian radial bases. The true unknown functions and their sieve approximations are allowed to be in general weighted function spaces with unbounded supports, which is important for time series…

用于宏观经济分析的贝叶斯神经网络AI 解读

Macroeconomic data is characterized by a limited number of observations (small T ), many time series (big K ) but also by featuring temporal dependence. Neural networks, by contrast, are designed for datasets with millions of observations and covariates. In this paper, we develop Bayesian neural networks (BNNs) that are well-suited for handling datasets commonly used for macroeconomic analysis in policy institutions. Our approach avoids extensive specification searches…

基于随机森林的分位数控制法AI 解读

This paper studies robust inference procedure for treatment effects in panel data with flexible relationship across units via the random forest method. The key contribution of this paper is twofold. First, we propose a direct construction of prediction intervals for the treatment effect by exploiting the information of the joint distribution of the cross-sectional units using random forest. In particular, we propose a Quantile Control Method (QCM) using the Quantile Random…

高维环境下的分布反事实分析AI 解读

In the context of treatment effect estimation, this paper proposes a new methodology to recover the counterfactual distribution when there is a single (or a few) treated unit and possibly a high-dimensional number of potential controls observed in a panel structure. The methodology accommodates, albeit does not require, the number of units to be larger than the number of time periods (high-dimensional setup). As opposed to model only the conditional mean, we propose to model…