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非齐次隐半马尔可夫与惩罚向量自回归的环境风险评估AI 解读

Motivated by the study of pollution trends in the city of Bergen, we introduce a flexible statistical framework for modeling multivariate air pollution data via a nonhomogeneous Hidden Semi-Markov Vector Auto-Regression. The hidden process captures unobserved environmental conditions, while the vector autoregressive structure accounts for temporal autocorrelation and cross-pollutant dependencies. The model further allows time-varying environmental conditions to influence…

双重下降：理解不可识别参数的线性模型估计与过拟合模型AI 解读

We consider ordinary least squares estimation and variations on least squares estimation such as penalized (regularized) least squares and spectral shrinkage estimates for problems with p > n and associated problems with prediction of new observations. After the introduction of Section 1, Section 2 examines a number of commonly used estimators for p > n. Section 3 introduces prediction with p > n. Section 4 introduces notational changes to facilitate discussion of…

截断现象的传输方法AI 解读

Substantial progress has recently been made in the understanding of the cutoff phenomenon for Markov processes, using an information-theoretic statistics known as varentropy [Sal23; Sal24; Sal25a; PS25]. In the present paper, we propose an alternative approach which bypasses the use of varentropy and exploits instead a new W-TV transport inequality, combined with a classical parabolic regularization estimate [BGL01; OV01]. While currently restricted to non-negatively curved…

加性全局Fréchet回归的变量选择AI 解读

We present a novel framework for variable selection in Fréchet regression with responses in general metric spaces, a setting increasingly relevant for analyzing non-Euclidean data such as probability distributions and covariance matrices. Building on the concept of (weak) Fréchet conditional means, we develop an additive regression model that represents the metric-based discrepancy of the response as a sum of covariate-specific nonlinear functions in reproducing kernel…

从预测算法到理论反例的自动生成AI 解读

How can we extract theoretical insights from machine learning algorithms? We take a familiar lesson: researchers often turn their intuitions into theoretical insights by constructing "anomalies" -- specific examples highlighting hypothesized flaws in a theory, such as the Allais paradox and the Kahneman-Tversky choice experiments for expected utility. We develop procedures that replace researchers' intuitions with predictive algorithms: given a predictive algorithm and a…

高维可加回归的极小极大最优迁移学习AI 解读

This paper studies high-dimensional additive regression under the transfer learning framework, where one observes samples from a target population together with auxiliary samples from different but potentially related regression models. We first introduce a target-only estimation procedure based on the smooth backfitting estimator with local linear smoothing. In contrast to previous work, we establish general error bounds under sub-Weibull($α$) noise, thereby accommodating…

基于样条从噪声数据中识别偏微分方程模型AI 解读

We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the cubic splines to estimate unobservable derivatives. The underlying PDE is based on a subset of these derivatives. This stage is computationally efficient: its computational complexity is a product of a constant with the sample size; this…

半参数三重差分估计量AI 解读

The triple difference causal inference framework is an extension of the well-known difference-in-differences framework. It relaxes the parallel trends assumption of the difference-in-differences framework through leveraging data from an auxiliary domain. Despite being commonly applied in empirical research, the triple difference framework has received relatively limited attention in the statistics literature. Specifically, investigating the intricacies of identification and…

利用函数型工具变量校正标量对函数回归偏差的最小二乘方法AI 解读

Instrumental variables are widely used to adjust for measurement error bias when assessing associations of health outcomes with ME prone independent variables. IV approaches addressing ME in longitudinal models are well established, but few methods exist for functional regression. We develop two methods to adjust for ME bias in scalar on function linear models. We regress a scalar outcome on an ME prone functional variable using a functional IV for model identification and…

小波–SARIMA–Transformer：降雨预测的混合模型AI 解读

This study develops and evaluates a novel hybridWavelet SARIMA Transformer, WST framework to forecast using monthly rainfall across five meteorological subdivisions of Northeast India over the 1971 to 2023 period. The approach employs the Maximal Overlap Discrete Wavelet Transform, MODWT with four wavelet families such as, Haar, Daubechies, Symlet, Coiflet etc. to achieve shift invariant, multiresolution decomposition of the rainfall series. Linear and seasonal components…

非凸梯度下降的长时间动力学与普适性AI 解读

This paper develops a general approach to characterize the long-time trajectory behavior of nonconvex gradient descent in generalized single-index models in the large aspect ratio regime. In this regime, we show that for each iteration the gradient descent iterate concentrates around a deterministic vector called the `Gaussian theoretical gradient descent', whose dynamics can be tracked by a state evolution system of two recursive equations for two scalars. Our concentration…

高维门槛回归模型中的一致推断AI 解读

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1 estimation errors for the Lasso estimator of the slope parameters and the threshold parameter, accommodating heteroskedastic non-subgaussian error terms and non-subgaussian covariates. Next, we derive the asymptotic distribution of tests…

基于KOO方法、带图结构的分组线性回归一致性聚类AI 解读

The kick-one-out (KOO) method is a variable selection method based on a model selection criterion. The method is very simple, and yet it has consistency in variable selection under a high-dimensional asymptotic framework with a specific model selection criterion. This paper proposes the join-twotogether (JTT) method, which is a clustering method based on the KOO method for group-wise linear regression with graph structure. The JTT method formulates the clustering problem as…

具有共同随机趋势的大规模曲线时间序列AI 解读

This paper studies high-dimensional curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor model for the latent curves with common trends. A functional PCA technique is applied to estimate the common stochastic trends and functional factor loadings. Under some regularity conditions we derive the mean square convergence and limit…

高维小样本下基于 GAT–CVAE 的抗异常值异质性处理效应估计AI 解读

We introduce a robust framework for heterogeneous treatment effect (HTE) estimation tailored to high-dimensional low sample size (HDLSS) settings. By combining Graph Attention Networks (GAT) to capture structural dependencies among confounders with a Conditional Variational Autoencoder (CVAE) for latent representation learning, our method expands the sample space and performs clustering that integrates even outlier sets into coherent subgroups. Clusterwise causal effects are…

多元模型中正则化估计的贝叶斯框架：融合近似计算概念AI 解读

This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding (quantization), thereby connecting two distinct paradigms: Bayesian inference and approximate computing. Next, Bayesian estimation of the means from two independent multivariate normal samples is employed to justify shrinkage estimators, i.e.,…

隐变量 DAG 中的平均因果效应估计：超越后门与前门准则AI 解读

The identification theory for causal effects in directed acyclic graphs (DAGs) with hidden variables is well established, but methods for estimating and inferring functionals that extend beyond the g-formula remain underdeveloped. Previous studies have introduced semiparametric estimators for such functionals in a broad class of DAGs with hidden variables. While these estimators exhibit desirable statistical properties such as double robustness in certain cases, they also…

高维非平稳时间序列的方差分析AI 解读

Temporal dependence and the resulting autocovariances in time series data can introduce bias into ANOVA test statistics, thereby affecting their size and power. This manuscript accounts for temporal dependence in ANOVA and develops a test statistic suitable for high-dimensional, non-stationary time series. Recognizing that the presence of complex fourth-order cumulants may introduce difficulties in variance estimation of the test statistic, we develop a bootstrap algorithm…

生存数据的双重稳健平均处理效应估计AI 解读

Considering censored outcomes in survival analysis can lead to quite complex results in the model setting of causal inference. Causal inference has attracted a lot of attention over the past few years, but little research has been done on survival analysis. Even for the only research conducted, the machine learning method was considered assuming a large sample, which is not suitable in that the actual data are high dimensional low sample size (HDLSS) method. Therefore,…

递归自适应划分估计器的统计-计算权衡AI 解读

Models based on recursive adaptive partitioning such as decision trees and their ensembles are popular for high-dimensional regression as they can potentially avoid the curse of dimensionality. Because empirical risk minimization (ERM) is computationally infeasible, these models are typically trained using greedy algorithms. Although effective in many cases, these algorithms have been empirically observed to get stuck at local optima. We explore this phenomenon in the…

带马蹄先验的贝叶斯可弯曲套索：缺失响应下GLM的交互效应建模AI 解读

Sparse regression problems, where the goal is to identify a small set of relevant predictors, often require modeling not only main effects but also meaningful interactions through other variables. While the pliable lasso has emerged as a powerful frequentist tool for modeling such interactions under strong heredity constraints, it lacks a natural framework for uncertainty quantification and incorporation of prior knowledge. In this paper, we propose a Bayesian pliable lasso…

灵活响应降维的非参数包络方法AI 解读

Envelope methods improve the estimation efficiency in multivariate linear regression by identifying and separating the material and immaterial parts of the responses or the predictors and estimating the regression coefficients using only the material part. Though envelopes have been extended to other models, such as GLMs, these extensions still largely fall under the restrictive parametric modeling framework. In this paper, we introduce a flexible, nonparametric extension of…

面向代谢物响应变量的营养信息贝叶斯变量选择模型AI 解读

Understanding the pathways through which diet affects human metabolism is a central task in nutritional epidemiology. This article proposes novel methodology to identify food items associated with blood metabolites in two cohorts of healthcare professionals. We analyze 30 food intake variables that exhibit relationship structure through their correlations and nutritional attributes. The metabolic responses include 244 compounds measured by mass spectrometry, presenting…

Largevars：检验大型 VAR 协整关系的 R 包AI 解读

Cointegration is a property of multivariate time series that determines whether its non-stationary, growing components have a stationary linear combination. Largevars R package conducts a cointegration test for high-dimensional vector autoregressions of order k based on the large N, T asymptotics of Bykhovskaya and Gorin (2022, 2025). The implemented test is a modification of the Johansen likelihood ratio test. In the absence of cointegration the test converges to the…