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基于奇异值分解与小波阈值的混频时间序列季节调整AI 解读

In this article, we propose a novel seasonal adjustment method that accommodates time series observed at mixed frequencies and possessing possibly multiple abrupt changes in seasonality. We assume that the observed series is a known linear transformation of an underlying high frequency series whose seasonal component can be represented as a matrix with a low rank Singular Value Decomposition (SVD) structure, and the nonseasonal component is difference stationary. The right…

GARCH-MIDAS 模型的自适应组 LASSOAI 解读

This article investigates the variable selection problem in the generalized autoregressive conditional heteroscedasticity-mixed-data sampling (GARCH-MIDAS) model of Engle, Ghysels, and Sohn (Citation2013), and establishes the corresponding theoretical properties along with a feasible computational algorithm. The proposed method is based on a penalized log-partial likelihood with an adaptively group-weighted L2 penalty on the long-term component coefficients. The variable…

重探伪逆：高维 Moore–Penrose 逆与岭型逆的渐近性质及应用AI 解读

In this paper, we derive high-dimensional asymptotic properties of the Moore–Penrose inverse and, as a byproduct, of various ridge-type inverses of the sample covariance matrix. In particular, the analytical expressions of the asymptotic behavior of the weighted sample trace moments of generalized inverse matrices are deduced in terms of the partial exponential Bell polynomials, which can be easily computed in practice. The existent results for pseudo-inverses are extended…

LASSO 及相关估计量的分布鲁棒预测误差AI 解读

We study the classical problem of predicting an outcome variable, Y, using a linear combination of a d-dimensional covariate vector, X. We are interested in linear predictors whose coefficients solve infβ∈Rd(EPn[|Y−X⊤β|r])1/r+δρ(β), where δ>0 is a regularization parameter, ρ:Rd→R+ is a convex penalty function, Pn is the empirical distribution of the data and r≥1. Our main contribution is a new bound on the out-of-distribution prediction error of such estimators. The new…

利用再现样本进行高维线性回归模型与系数的有限样本及大样本推断AI 解读

In this paper, we present a novel and effective inference approach to conduct both finite and large sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in which we conduct statistical inference by creating and studying the behavior of artificial samples that are obtained by mimicking the sampling mechanism of the data. We construct confidence sets for (a) the true model corresponding to the…

正则化M估计量装袋集成的精确渐近分析AI 解读

We characterize the squared prediction risk of ensemble estimators obtained through subagging (subsample bootstrap aggregating) regularized M-estimators and construct a consistent estimator for the risk. Specifically, we consider a heterogeneous collection of M≥1 regularized M-estimators, each trained with (possibly different) subsample sizes, convex differentiable losses, and convex regularizers. We operate under the proportional asymptotics regime, where the sample size n,…

含未观测异质性的大型面板多重结构突变估计AI 解读

This article proposes a novel algorithm to identify potentially multiple breaks in linear panel data models, while the slope coefficients can have individual heterogeneity and the cross-sectional dimension is allowed to diverge jointly with the time span. The algorithm adopts a shrinkage penalty to detect breaks, and delivers a consistent estimator for the number of breaks and fraction-consistent estimators for break dates. In the presence of latent grouped heterogeneity, we…

利用因子斜率的低秩估计推断异质效应AI 解读

Abstract We study a panel data model with heterogeneous effects, allowing slopes to vary across individuals and time. To reduce dimensionality, we assume these slopes follow a factor structure, so slope matrices can be estimated via low-rank regularized regression. We propose a multi-step estimation procedure incorporating sample splitting and partialing-out to enable valid inference after penalized estimation. We establish the asymptotic normality of the resulting…

稀疏高斯化典型相关分析及其投资组合应用AI 解读

Canonical correlation analysis (CCA) is an important statistical technique that explores the linear relationships between two sets of variables. In this article, we propose a new generalization of CCA named sparse Gaussianized CCA (SGCCA) for high-dimensional data analysis. SGCCA has a number of favorable properties. First, it is conceptually easy to comprehend and efficient to implement. Second, it not only yields sparse and nested canonical vectors, but is also invariant…

张量数据的扩散指数预测AI 解读

In this paper, we consider diffusion index forecasting with both tensor and non-tensor predictors, where the tensor structure is preserved with a Canonical Polyadic (CP) tensor factor model. When the number of non-tensor predictors is small, we study the asymptotic properties of the least squares estimator in this tensor factor-augmented regression, allowing for factors with different strengths. We derive an analytical formula for prediction intervals that accounts for the…

高维条件因子模型AI 解读

This paper studies estimation and variable selection in conditional factor models with high-dimensional instruments, where the coefficient matrix exhibits a low-rank and row-sparse structure. We propose a multi-stage estimation procedure that combines nuclear norm regularization and adaptive group LASSO regression to consistently estimate latent factors and row-sparse loading coefficients, while selecting relevant instrumental characteristics. We establish theoretical…

分布目标下最优政策学习的公平性正则化AI 解读

A decision maker typically (i) incorporates training data to learn about the relative effectiveness of treatments, and (ii) chooses an implementation mechanism that implies an “optimal” predicted outcome distribution according to some target functional. Nevertheless, a fairness-aware decision maker may not be satisfied achieving said optimality at the cost of being “unfair” against a subgroup of the population, in the sense that the outcome distribution in that subgroup…

基于广义特征值的高维稀疏回归方向识别与极小极大估计AI 解读

In high-dimensional (HD) sparse linear regression, parameter selection and estimation are addressed using a constraint $l_0$ on the direction of the parameter vector. We begin by establishing a general result that identifies this direction through the leading generalized eigenspace of specific measurable matrices. Using this result, we propose a novel approach to the selection of the best subsets by solving an empirical generalized eigenvalue problem to estimate the…

维度与样本量成比例时逻辑回归的 Diaconis–Ylvisaker 先验惩罚似然AI 解读

Summary We characterize the behaviour of the maximum Diaconis–Ylvisaker prior penalized likelihood estimator in high-dimensional logistic regression, where the number of covariates is a fraction $ \kappa\in(0,1) $ of the number of observations $ n $, as $ n\to\infty $. We construct a rescaled estimator with zero asymptotic aggregate bias, and define adjusted $ Z $-statistics and rescaled penalized likelihood ratio statistics that exhibit the typical null asymptotic…

通过成对似然截断估计高维协方差AI 解读

Summary Pairwise likelihood is an approximation of the full likelihood function that facilitates the analysis of high-dimensional covariance models. By combining marginal bivariate likelihoods, it effectively simplifies high-dimensional dependencies, making the estimation process more manageable. We introduce estimation of sparse high-dimensional covariance matrices by maximizing a truncated version of the pairwise likelihood function, obtained by including pairwise terms…

稀疏高阶偏最小二乘：变量选择、降维与张量去噪AI 解读

Abstract Motivated by the challenge of estimating effects of DNA methylation on 3D genomic contacts captured by multimodal single-cell Hi-C data, we consider the tensor-response partial least squares model with $ \mathcal{Y}=\mathcal{B}\times_{1}X+\mathcal{F} $, where the correlated high-dimensional predictors $ X\in\mathbb{R}^{n\times d_{1}} $ and the sparse and noisy high-dimensional responses $ \mathcal{Y}\in\mathbb{R}^{n\times\prod_{m}d_{m}} $ are observed, the low-rank…

高维分位数回归的通信高效估计与分布式预言机估计AI 解读

In this article, we present a novel communication-efficient estimator for distributed high-dimensional quantile regression with folded-concave penalties. An Iterative Multi-Step Algorithm (IMSA) is employed to tackle the nonconvex challenge of the objective function, taking into account both the statistical accuracy and the communication constraints. We demonstrate that the proposed IMSA estimators share similar properties with the global folded-concave penalized estimator.…

协变量漂移下核岭回归的伪标签方法AI 解读

We develop and analyze a principled approach to kernel ridge regression under covariate shift. The goal is to learn a regression function with small mean squared error over a target distribution, based on unlabeled data from there and labeled data that may have a different feature distribution. We propose to split the labeled data into two subsets, and conduct kernel ridge regression on them separately to obtain a collection of candidate models and an imputation model. We…

泊松经验贝叶斯估计：何时先验建模优于边际建模？AI 解读

Empirical Bayes (EB) is a popular framework for large-scale inference that aims to find data-driven estimators to compete with the Bayesian oracle that knows the true prior. Two principled approaches to EB estimation have emerged over the years: f-modeling, which constructs an approximate Bayes rule by estimating the marginal distribution of the data, and g-modeling, which estimates the prior from data and then applies the learned Bayes rule. For the Poisson model, the…

利用正则化后分布回归评估最低工资的分布效应AI 解读

Summary We evaluate the distributional effects of a minimum wage introduction based on a dataset with a moderate sample size, but a large number of potential covariates. In this context, the selection of relevant control variables at each distributional threshold is crucial to test hypotheses about the impact of the continuous treatment variable. To this end, we use a post-double-selection logistic distribution regression approach, which allows for uniformly valid inference…

主成分分析能否保留因子载荷的稀疏性？AI 解读

This article studies the principal component analysis (PCA) estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PCA estimators of loadings, which comes from the approximately (block) upper triangular structure of the rotation matrix. It suggests an asymmetric relationship among factors: the sparsity of the rotated loadings for a stronger factor can be contaminated by the loadings from weaker ones, but the…

PALAR：用相对丰度预测变量估计绝对丰度回归效应AI 解读

High-dimensional compositional data are ubiquitous in omics research. Microbiome sequencing experiments measure the relative abundances (proportions) of microbial features, while the absolute abundances within the ecosystem remain unobserved. Most regression methods with microbial relative abundance predictors rely on log-ratio transformations and typically impose sparsity on the regression coefficients to manage high dimensionality. However, we show that the sparsity…

深度离散编码器：具有离散潜在层的可识别深度生成模型AI 解读

In the era of generative AI, deep generative models (DGMs) with latent representations have gained tremendous popularity. Despite their impressive empirical performance, the statistical properties of these models remain underexplored. DGMs are often overparametrized, non-identifiable, and uninterpretable black boxes, raising serious concerns when deploying them in high-stakes applications. Motivated by this, we propose interpretable deep generative models for rich data types…

大型加性潜变量模型的统计分位数学习AI 解读

Large and complex datasets, emerging from technological advancements in fields such as genomics and brain imaging, hold ample promise for gaining new scientific insights. Yet, their inherent nonlinearity and high dimensionality present considerable theoretical, methodological, and application challenges to the statistics and machine learning community. This article introduces Statistical Quantile Learning (SQL), a new nonparametric method for estimating large additive latent…