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非可分面板模型的低秩近似AI 解读

Summary We provide estimation methods for nonseparable panel models based on low-rank factor structure approximations. The factor structures are estimated by matrix-completion methods to deal with the computational challenges of principal component analysis in the presence of missing data. We show that the resulting estimators are consistent in large panels, but suffer from approximation and shrinkage biases. We correct these biases using matching and…

多工具变量下的完全子集平均AI 解读

Summary We propose a two-stage least squares (2SLS) estimator whose first stage is the equal-weighted average over a complete subset with k instruments among K available, which we call the complete subset averaging (CSA) 2SLS. The approximate mean squared error (MSE) is derived as a function of the subset size k by the Nagar (1959) expansion. The subset size is chosen by minimising the sample counterpart of the approximate MSE. We show that this method achieves asymptotic…

利用横截面均值增广时间序列回归进行预测AI 解读

Summary There is a large and growing body of literature concerned with forecasting time series variables by the use of factor-augmented regression models. The workhorse of this literature is a two-step approach in which the factors are first estimated by applying the principal components method to a large panel of variables, and the forecast regression is then estimated, conditional on the first-step factor estimates. Another stream of research that has attracted much…

删失数据下重复事件动态模型的估计AI 解读

Summary In this paper, we consider estimation of dynamic models of recurrent events (event histories) in continuous time using censored data. We develop maximum simulated likelihood estimators where missing data are integrated out using Monte Carlo and importance sampling methods. We allow for random effects and integrate out this unobserved heterogeneity using a quadrature rule. In Monte Carlo experiments, we find that maximum simulated likelihood estimation is practically…

条件平均处理效应及其他因果函数的去偏机器学习AI 解读

Summary This paper provides estimation and inference methods for the best linear predictor (approximation) of a structural function, such as conditional average structural and treatment effects, and structural derivatives, based on modern machine learning tools. We represent this structural function as a conditional expectation of an unbiased signal that depends on a nuisance parameter, which we estimate by modern machine learning techniques. We first adjust the signal to…

基于平滑分位数回归的简便面板分位数模型估计量AI 解读

Summary This paper considers panel data models where the idiosyncratic errors are subject to conditonal quantile restrictions. We propose a two-step estimator based on smoothed quantile regressions that is easy to implement. The asymptotic distribution of the estimator is established, and the analytical expression of its asymptotic bias is derived. Building on these results, we show how to make asymptotically valid inference on the basis of both analytical and split-panel…

带交互固定效应的面板VAR模型AI 解读

Summary In the literature, a common feature of panel models with interactive fixed effects is that they model a univariate variable. In this regard, they are incapable of addressing dynamic and simultaneous interactions among a set of macroeconomic variables, a problem that falls within the realm of structural analysis. This paper aims to contribute to the existing literature by studying a homogeneous panel vector autoregression (VAR) model with interactive fixed effects.…

SuperMix：混合模型的稀疏正则化AI 解读

This paper investigates the statistical estimation of a discrete mixing measure μ0 involved in a kernel mixture model. Using some recent advances in ℓ1-regularization over the space of measures, we introduce a “data fitting and regularization” convex program for estimating μ0 in a grid-less manner from a sample of mixture law, this method is referred to as Beurling-LASSO. Our contribution is two-fold: we derive a lower bound on the bandwidth of our data fitting term…

重尾模型中的因果发现AI 解读

Causal questions are omnipresent in many scientific problems. While much progress has been made in the analysis of causal relationships between random variables, these methods are not well suited if the causal mechanisms only manifest themselves in extremes. This work aims to connect the two fields of causal inference and extreme value theory. We define the causal tail coefficient that captures asymmetries in the extremal dependence of two random variables. In the population…

时间与空间依赖下的 LASSO 推断AI 解读

We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak temporal dependence. A sequence of regressions with many regressors using LASSO (Least Absolute Shrinkage and Selection Operator) is applied for variable selection purpose, and an overall penalty level is carefully chosen by a block multiplier bootstrap…

因子驱动的双区制回归AI 解读

We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show that the optimization problem can be reformulated as mixed integer optimization, and we present two alternative computational algorithms. We derive the asymptotic distribution of the resulting estimator under the scheme that the threshold…

单纯形的统计学习：重访解混问题AI 解读

We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of “spectral unmixing.” We theoretically show that a sufficient sample complexity for reliable learning of a K-dimensional simplex up to a total-variation error of ϵ is O(K2ϵlogKϵ), which yields…

高维 Kendall 秩相关矩阵线性谱统计量的中心极限定理及应用AI 解读

This paper is concerned with the limiting spectral behaviors of large dimensional Kendall’s rank correlation matrices generated by samples with independent and continuous components. The statistical setting in this paper covers a wide range of highly skewed and heavy-tailed distributions since we do not require the components to be identically distributed, and do not need any moment conditions. We establish the central limit theorem (CLT) for the linear spectral statistics…

高维稀疏二次判别分析的凸优化方法AI 解读

In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for the classification error. Minimax lower bounds are established to demonstrate the necessity of structural assumptions such as sparsity conditions on the discriminating direction and differential graph for the possible construction of consistent high-dimensional QDA rules. We then propose a classification algorithm called SDAR using…

稀疏高维加性模型中的统计推断AI 解读

In this paper, we discuss the estimation of a nonparametric component f1 of a nonparametric additive model Y=f1(X1)+⋯+fq(Xq)+ϵ. We allow the number q of additive components to grow to infinity and we make sparsity assumptions about the number of nonzero additive components. We compare this estimation problem with that of estimating f1 in the oracle model Z=f1(X1)+ϵ, for which the additive components f2,…,fq are known. We construct a two-step presmoothing-and-resmoothing…

一般谱主体下线性混合模型的主成分AI 解读

We study the principal components of covariance estimators in multivariate mixed-effects linear models. We show that, in high dimensions, the principal eigenvalues and eigenvectors may exhibit bias and aliasing effects that are not present in low-dimensional settings. We derive the first-order limits of the principal eigenvalue locations and eigenvector projections in a high-dimensional asymptotic framework, allowing for general population spectral distributions for the…

因果自助法AI 解读

The bootstrap, introduced by The Jackknife, the Bootstrap and Other Resampling Plans ((1982), SIAM), has become a very popular method for estimating variances and constructing confidence intervals. A key insight is that one can approximate the properties of estimators by using the empirical distribution function of the sample as an approximation for the true distribution function. This approach views the uncertainty in the estimator as coming exclusively from sampling…

长记忆过程的频域自助法AI 解读

The aim of the paper is to describe a bootstrap, contrary to the sieve bootstrap, valid under either long memory (LM) or short memory (SM) dependence. One of the reasons of the failure of the sieve bootstrap in our context is that under LM dependence, the sieve bootstrap may not be able to capture the true covariance structure of the original data. We also describe and examine the validity of the bootstrap scheme for the least squares estimator of the parameter in a…

通过分布鲁棒优化学习表现稳定的模型AI 解读

A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts or unmodeled temporal effects. We develop and analyze a distributionally robust stochastic optimization (DRO) framework that learns a model providing good performance against perturbations to the data-generating distribution. We give a convex formulation for the problem, providing…

白噪声回归中的框架约束总变差正则化AI 解读

Despite the popularity and practical success of total variation (TV) regularization for function estimation, surprisingly little is known about its theoretical performance in a statistical setting. While TV regularization has been known for quite some time to be minimax optimal for denoising one-dimensional signals, for higher dimensions this remains elusive until today. In this paper, we consider frame-constrained TV estimators including many well-known (overcomplete)…

基于伪似然的贝叶斯向量自回归模型强选择一致性AI 解读

Vector autoregressive (VAR) models aim to capture linear temporal interdependencies among multiple time series. They have been widely used in macroeconomics and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which will provide novel insights into the role of temporal dependence for…

稀疏向量模型中的自适应稳健估计AI 解读

For the sparse vector model, we consider estimation of the target vector, of its ℓ2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with respect to the triplet “noise level—noise distribution—sparsity.” We consider classes of noise distributions with polynomially and exponentially decreasing tails as well as the case of Gaussian noise. The obtained rates turn out to be…

高维交叉验证Lasso的理论分析AI 解读

In this paper, we derive nonasymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using K-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly optimal rates of convergence in the prediction, L2, and L1 norms. For example, we show that in the model with the Gaussian noise and under fairly general assumptions on the candidate set of values of the penalty parameter, the estimation error of…

重尾数据的收缩原则：高维稳健低秩矩阵恢复AI 解读

This paper introduces a simple principle for robust statistical inference via appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the distributional conditions from subexponential or sub-Gaussian to more relaxed bounded second or fourth moment. As an illustration of this principle, we focus on robust estimation of the low-rank matrix Θ∗ from the trace regression model Y=Tr(Θ∗⊤X)+ε. It encompasses four popular problems: sparse…