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最优处理分配下福利与价值泛函的推断AI 解读

We provide theoretical results for the estimation and inference of a class of welfare and value functionals of the nonparametric conditional average treatment effect (CATE) function under optimal treatment assignment, i.e., treatment is assigned to an observed type if and only if its CATE is nonnegative. For the optimal welfare functional defined as the average value of CATE on the subpopulation with nonnegative CATE, we establish the $\sqrt{n}$ asymptotic normality of the…

基于核回归的迁移学习AI 解读

In recent years, transfer learning has garnered significant attention. Its ability to leverage knowledge from related studies to improve generalization performance in a target study has made it highly appealing. This paper focuses on investigating the transfer learning problem within the context of nonparametric regression over a reproducing kernel Hilbert space. The aim is to bridge the gap between practical effectiveness and theoretical guarantees. We specifically consider…

机器学习辅助的回归函数比较AI 解读

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing approaches typically rely on smoothing techniques and are thus hindered by the curse of dimensionality. We propose a generalized notion of kernel-based conditional mean dependence that provides a new characterization of the null hypothesis of…

相关误差下函数数据表示的快速贝叶斯基选择AI 解读

Functional data analysis finds widespread application across various fields. While functional data are intrinsically infinite-dimensional, in practice, they are observed only at a finite set of points, typically over a dense grid. As a result, smoothing techniques are often used to approximate the observed data as functions. In this work, we propose a novel Bayesian approach for selecting basis functions for smoothing one or multiple curves simultaneously. Our method…

利用语义相似性开展人工智能生成处理的实验AI 解读

Large Language Models (LLMs) enable a new form of digital experimentation where treatments combine human and model-generated content in increasingly sophisticated ways. The main methodological challenge in this setting is representing these high-dimensional treatments without losing their semantic meaning or rendering analysis intractable. Here, we address this problem by focusing on learning low-dimensional representations that capture the underlying structure of such…

学生化中位数的 m-out-of-n 自助估计：中心极限定理与 Edgeworth 展开AI 解读

The m-out-of-n bootstrap, originally proposed by Bickel, Gotze, and Zwet (1992), approximates the distribution of a statistic by repeatedly drawing m subsamples (with m much smaller than n) without replacement from an original sample of size n. It is now routinely used for robust inference with heavy-tailed data, bandwidth selection, and other large-sample applications. Despite its broad applicability across econometrics, biostatistics, and machine learning, rigorous…

多层函数混合效应模型中的固定效应与随机效应变量选择AI 解读

We develop a new method for simultaneously selecting fixed and random effects in a multilevel functional regression model. The proposed method is motivated by accelerometer-derived physical activity data from the 2011-12 cohort of the National Health and Nutrition Examination Survey (NHANES), where we are interested in identifying age and race-specific heterogeneity in covariate effects on the diurnal patterns of physical activity across the lifespan. Existing methods for…

SCMD：量化跨环境可迁移性的结构因果模型核距离AI 解读

Out-of-distribution generalization is key to building models that remain reliable across diverse environments. Recent causality-based methods address this challenge by learning invariant causal relationships in the underlying data-generating process. Yet, measuring how causal structures differ across environments, and the resulting generalization difficulty, remains difficult. To tackle this challenge, we propose the Structural Causal Model Distance (SCMD), a principled…

急救医疗服务中涌现的动态空间边界：从基本原理出发的 Navier–Stokes 框架AI 解读

Emergency medical services (EMS) response times are critical determinants of patient survival, yet existing approaches to spatial coverage analysis rely on discrete distance buffers or ad-hoc geographic information system (GIS) isochrones without theoretical foundation. This paper derives continuous spatial boundaries for emergency response from first principles using fluid dynamics (Navier-Stokes equations), demonstrating that response effectiveness decays exponentially…

数据融合下因果剂量反应函数的估计AI 解读

Estimating the causal dose-response function is challenging, particularly when data from a single source are insufficient to estimate responses precisely across all exposure levels. To overcome this limitation, we propose a data fusion framework that leverages multiple data sources that are partially aligned with the target distribution. Specifically, we derive a Neyman-orthogonal loss function tailored for estimating the dose-response function within data fusion settings.…

空间处理效应边界的非参数识别：银行网点整合的证据AI 解读

I develop a nonparametric framework for identifying spatial boundaries of treatment effects without imposing parametric functional form restrictions. The method employs local linear regression with data-driven bandwidth selection to flexibly estimate spatial decay patterns and detect treatment effect boundaries. Monte Carlo simulations demonstrate that the nonparametric approach exhibits lower bias and correctly identifies the absence of boundaries when none exist, unlike…

空间处理效应边界的非参数识别与估计：四千二百万条污染观测的证据AI 解读

This paper develops a nonparametric framework for identifying and estimating spatial boundaries of treatment effects in settings with geographic spillovers. While atmospheric dispersion theory predicts exponential decay of pollution under idealized assumptions, these assumptions -- steady winds, homogeneous atmospheres, flat terrain -- are systematically violated in practice. I establish nonparametric identification of spatial boundaries under weak smoothness and…

未观测混杂下利用代理变量发现因果关系AI 解读

Inferring causal relationships between variable pairs in the observational study is crucial but challenging, due to the presence of unmeasured confounding. While previous methods employed the negative controls to adjust for the confounding bias, they were either restricted to the discrete setting (i.e., all variables are discrete) or relied on strong assumptions for identification. To address these problems, we develop a general nonparametric approach that accommodates both…

基于签名度量的路径空间局部回归AI 解读

We study nonparametric regression and classification for path-valued data. We introduce a functional Nadaraya-Watson estimator that combines the signature transform from rough path theory with local kernel regression. The signature transform provides a principled way to encode sequential data through iterated integrals, enabling direct comparison of paths in a natural metric space. Our approach leverages signature-induced distances within the classical kernel regression…

高维回归中的自适应影响诊断AI 解读

An adaptive Cook's distance (ACD) for diagnosing influential observations in high-dimensional single-index models with multicollinearity and outlier contamination is proposed. ACD is a model-free technique built on sparse local linear gradients to temper leverage effects. In simulations spanning low- and high-dimensional design settings with strong correlation, ACD based on LASSO (ACD-LASSO) and SCAD (ACD-SCAD) penalties reduced masking and swamping relative to classical…

利用高度自适应 Lasso 构造无限维函数参数的置信区间AI 解读

Estimating the conditional mean function is a central task in statistical learning. In this paper, we consider estimation and inference for a nonparametric class of real-valued cadlag functions with bounded sectional variation (Gill et al., 1995), using the Highly Adaptive Lasso (HAL) (van der Laan, 2015; Benkeser and van der Laan, 2016; van der Laan, 2023), a flexible empirical risk minimizer over linear combinations of tensor products of zero- or higher-order spline basis…

核设定检验的有限样本失真：经验方向分量的扰动分析AI 解读

This paper provides a new theoretical lens for understanding the finite-sample performance of kernel-based specification tests, such as the Kernel Conditional Moment (KCM) test. Rather than introducing a fundamentally new test, we isolate and rigorously analyze the finite-sample distortion arising from the discrepancy between the empirical and population eigenspaces of the kernel operator. Using perturbation theory for compact operators, we demonstrate that the estimation…

连续稀疏正则化中的有效区域与核：在草图混合模型中的应用AI 解读

This paper advances the general theory of continuous sparse regularisation on measures with the Beurling-LASSO (BLASSO). This TV-regularised convex program on the space of measures allows to recover a sparse measure using a noisy observation from a measurement operator. While previous works have uncovered the central role played by this operator and its associated kernel in order to get estimation error bounds, the latter requires a technical local positive curvature (LPC)…

样本量依赖核的高维U统计量高斯近似AI 解读

Motivated by small bandwidth asymptotics for kernel-based semiparametric estimators in econometrics, this paper establishes Gaussian approximation results for high-dimensional fixed-order $U$-statistics whose kernels depend on the sample size. Our results allow for a situation where the dominant component of the Hoeffding decomposition is absent or unknown, including cases with known degrees of degeneracy as special forms. The obtained error bounds for Gaussian…

带协变量的非负矩阵分解用于标签矩阵分类AI 解读

Non-negative matrix factorization (NMF) is widely used for dimensionality reduction and interpretable analysis, but standard formulations are unsupervised and cannot directly exploit class labels. Existing supervised or semi-supervised extensions usually incorporate labels only via penalties or graph constraints, still requiring an external classifier. We propose \textit{NMF-LAB} (Non-negative Matrix Factorization for Label Matrix), which redefines classification as the…

断点回归的边界估计：基于成绩与经济需要的助学项目证据AI 解读

In the conventional regression-discontinuity (RD) design, the probability that units receive a treatment changes discontinuously as a function of one covariate exceeding a threshold or cutoff point. This paper studies an extended RD design where assignment rules simultaneously involve two or more continuous covariates. We show that assignment rules with more than one variable allow the estimation of a more comprehensive set of treatment effects, relaxing in a research-driven…

HAC 估计的自动阶数与带宽选择及特征值调整缺陷AI 解读

In this paper, we propose a new heteroskedasticity and autocorrelation consistent covariance matrix estimator based on the prewhitened kernel estimator and a localized leave-one-out frequency domain cross-validation (FDCV). We adapt the cross-validated log likelihood (CVLL) function to simultaneously select the order of the prewhitening vector autoregression (VAR) and the bandwidth. The prewhitening VAR is estimated by the Burg method without eigen adjustment as we find the…

机器学习、偏微分方程与统计中的再生核方法AI 解读

This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite kernels; discrete and continuous RKHS; kernel engineering and scaling maps; error assessment via kernel discrepancy/maximum mean discrepancy (MMD); and a systematic operator view of kernels. In this viewpoint, projection, gradient,…

二次渐近机制下核随机矩阵与核回归的普适性AI 解读

Kernel ridge regression (KRR) is a popular class of machine learning models that has become an important tool for understanding deep learning. Much of the focus thus far has been on studying the proportional asymptotic regime, $n \asymp d$, where $n$ is the number of training samples and $d$ is the dimension of the dataset. In the proportional regime, under certain conditions on the data distribution, the kernel random matrix involved in KRR exhibits behavior akin to that of…