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异质依赖数据下固定设计核平均的一致收敛AI 解读

We provide uniform convergence rates for kernel averages on $[0,1]$ under equally-spaced fixed design points of the form $x_{t,T}=t/T,\ t\in\{1,\dotsc, T\},\ T\in\mathbb{N}$. The rates of weak and strong uniform consistency are derived under strong mixing and moment conditions and do not require stationarity. The analysis exploits the grid structure and thus complements existing random-design results such as those of Hansen (2008) and Kristensen (2009), which rely on…

空间 HAC 标准误的带宽选择AI 解读

Spatial autocorrelation in regression models can lead to downward biased standard errors and thus incorrect inference. The most common correction in applied economics is the spatial heteroskedasticity and autocorrelation consistent (HAC) standard error estimator introduced by Conley (1999). A critical input is the kernel bandwidth: the distance within which residuals are allowed to be correlated. However, this is still an unresolved problem and there is no formal guidance in…

回归不连续设计中直接估计条件平均处理效应的贝叶斯加性回归树AI 解读

Regression discontinuity designs (RDD) are widely used for causal inference. In many empirical applications, treatment effects vary substantially with covariates, and ignoring such heterogeneity can lead to misleading conclusions, which motivates flexible modeling of heterogeneous treatment effects in RDD. To this end, we propose a Bayesian nonparametric approach to estimating heterogeneous treatment effects based on Bayesian Additive Regression Trees (BART). The key feature…

目标偏移下正则化最小二乘的重要性加权校正AI 解读

Importance weighting is a standard tool for correcting distribution shift, but its statistical behavior under target shift -- where the label distribution changes between training and testing while the conditional distribution of inputs given the label remains stable -- remains under-explored. We analyze importance-weighted kernel ridge regression under target shift and show that, because the weights depend only on the output variable, reweighting corrects the train-test…

平滑样条 ANOVA 模型中导数的估计与假设检验AI 解读

Within the framework of smoothing spline ANOVA, we propose a plug-in kernel ridge regression estimator to estimate the derivatives of the underlying multivariate regression function. We first establish an $L_\infty$ convergence rate of the proposed estimator under general random designs. When the covariates are uniformly distributed, we provide a in-depth analysis that includes a sharp upper bound and the minimax lower bound of the $L_2$ convergence rate. Additionally,…

用于交错政策实施评估的可交换高斯过程AI 解读

We study the use of exchangeable multi-task Gaussian processes (GPs) for causal inference in panel data, applying the framework to two settings: one with a single treated unit subject to a once-and-for-all treatment and another with multiple treated units and staggered treatment adoption. Our approach models the joint evolution of outcomes for treated and control units through a GP prior that ensures exchangeability across units while allowing for flexible nonlinear trends…

利用核岭回归实现最优且结构自适应的条件处理效应估计AI 解读

We propose an optimal algorithm for estimating conditional average treatment effects (CATEs) when response functions lie in a reproducing kernel Hilbert space (RKHS). We study settings in which the contrast function is structurally simpler than the nuisance functions: (i) it lies in a lower-complexity RKHS with faster eigenvalue decay, (ii) it satisfies a source condition relative to the nuisance kernel, or (iii) it depends on a known low-dimensional covariate…

HAL-MLE 对数样条密度估计（第一部分：单变量）AI 解读

We study nonparametric maximum likelihood estimation of probability densities under a total variation (TV) type penalty, sectional variation norm (also named as Hardy-Krause variation). TV regularization has a long history in regression and density estimation, including results on $L^2$ and KL divergence convergence rates. Here, we revisit this task using the Highly Adaptive Lasso (HAL) framework. We formulate a HAL-based maximum likelihood estimator (HAL-MLE) using the…

线性矩条件准贝叶斯推断的改进延迟接受 MCMCAI 解读

We develop a computationally efficient framework for quasi-Bayesian inference based on linear moment conditions. The approach employs a delayed acceptance Markov chain Monte Carlo (DA-MCMC) algorithm that uses a surrogate target kernel and a proposal distribution derived from an approximate conditional posterior, thereby exploiting the structure of the quasi-likelihood. Two implementations are introduced. DA-MCMC-Exact fully incorporates prior information into the proposal…

核模型中的特征学习理论AI 解读

We study feature learning in a compositional variant of kernel ridge regression in which the predictor is applied to a learnable linear transformation of the input. When the response depends on the input only through a low-dimensional predictive subspace, we show that all global minimizers of the population objective for the linear transformation annihilate directions orthogonal to this subspace, and in certain regimes, exactly identify the subspace. Moreover, we show that…

带微分正则化的空间比例风险模型AI 解读

The Proportional Hazards (PH) model is one of the most widely used models in survival analysis, typically assuming a log-linear relationship between covariates and the hazard function. However, in the context of spatial survival data, where the time-to-event variable is associated with a spatial location within a given domain, this assumption is often unrealistic in capturing spatial effects. Thus, this paper proposes modeling the location effect through a nonparametric…

熵正则化推断：一种预测视角AI 解读

Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from information to reported predictive distributions, and impose three structural requirements on evaluation: locality, strict propriety, and coherence under aggregation (coarsening/refinement) of outcome categories. These axioms characterize…

基于核方法的最优加权保形时间序列预测AI 解读

In this work, we present a novel conformal prediction method for time-series, which we call Kernel-based Optimally Weighted Conformal Prediction Intervals (KOWCPI). Specifically, KOWCPI adapts the classic Reweighted Nadaraya-Watson (RNW) estimator for quantile regression on dependent data and learns optimal data-adaptive weights. Theoretically, we tackle the challenge of establishing a conditional coverage guarantee for non-exchangeable data under strong mixing conditions on…

植被绿度驱动因素的空间变量选择：面向 MODIS 植被指数AI 解读

Understanding how environmental drivers relate to vegetation condition motivates spatially varying regression models, but estimating a separate coefficient surface for every predictor can yield noisy patterns and poor interpretability when many predictors are irrelevant. Motivated by MODIS vegetation index studies, we examine predictors from spectral bands, productivity and energy fluxes, observation geometry, and land surface characteristics. Because these relationships…

两阶段数据合成：隐私与预测之间由统计驱动的受限权衡AI 解读

Synthetic data have gained increasing attention across various domains, with a growing emphasis on their performance in downstream prediction tasks. However, most existing synthesis strategies focus on maintaining statistical information. Although some studies address prediction performance guarantees, their single-stage synthesis designs make it challenging to balance the privacy requirements that necessitate significant perturbations and the prediction performance that is…

高维重尾局部平稳时间序列的稀疏学习：集中与预言不等式AI 解读

Sparse learning is ubiquitous in many machine learning tasks. It aims to regularize the goodness-of-fit objective by adding a penalty term to encode structural constraints on the model parameters. In this paper, we develop a flexible sparse learning framework tailored to high-dimensional heavy-tailed locally stationary time series (LSTS). The data-generating mechanism incorporates a regression function that changes smoothly over time and is observed under noise belonging to…

利用有效工具变量与机器学习推断异质处理效应AI 解读

We introduce a new instrumental variable (IV) estimator for heterogeneous treatment effects in the presence of endogeneity. Our estimator is based on double/debiased machine learning (DML) and uses efficient machine learning instruments (MLIV) and kernel smoothing. We prove consistency and asymptotic normality of our estimator and also construct confidence sets that are more robust towards weak IV. Along the way, we also provide an accessible discussion of the corresponding…

神经网络机器回归：揭示高阶协同效应的深度学习框架AI 解读

We propose a new neural network framework, termed Neural Network Machine Regression (NNMR), which integrates trainable input gating and adaptive depth regularization to jointly perform feature selection and function estimation in an end-to-end manner. By penalizing both gating parameters and redundant layers, NNMR yields sparse and interpretable architectures while capturing complex nonlinear relationships driven by high-order synergistic effects. We further develop a…

面向协变量偏移下函数型数据的正则化学习AI 解读

This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate shift occurs when the input distributions of the training and test data differ, introducing significant challenges for reliable learning. By restricting the hypothesis space, we develop a practical operator learning algorithm capable of…

非参数回归中的部分异方差反卷积估计AI 解读

In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the measurement errors are heteroscedastic. We propose a kernel-based estimator of the regression function in this framework and show that it achieves the optimal convergence rate under suitable regularity conditions. The finite-sample…

基于地标超级模型与提升树的时间依赖协变量事件史分析AI 解读

We propose a nonparametric method for dynamic prediction in event history analysis with high-dimensional, time-dependent covariates. The approach estimates future conditional hazards by combining landmarking supermodels with gradient boosted trees. Unlike joint modeling or Cox landmarking models, the proposed estimator flexibly captures interactions and nonlinear effects without imposing restrictive parametric assumptions or requiring the covariate process to be Markovian.…

用核回归估计线性模型中不同光滑度的时变参数AI 解读

We study kernel-based estimation of nonparametric time-varying parameters (TVPs) in linear models. Our contributions are threefold. First, we establish consistency and asymptotic normality of the kernel-based estimator for a broad class of TVPs including deterministic smooth functions, the rescaled random walk, structural breaks, the threshold model and their mixtures. Our analysis exploits the smoothness of the TVP. Second, we show that the bandwidth rate must be determined…

基于核方法的非参数形状约束检验AI 解读

We propose a kernel-based nonparametric framework for mean-variance optimization that enables inference on economically motivated shape constraints in finance, including positivity, monotonicity, and convexity. Many central hypotheses in financial econometrics are naturally expressed as shape relations on latent functions (e.g., term premia, CAPM relations, and the pricing kernel), yet enforcing such constraints during estimation can mask economically meaningful violations;…

多维断点回归设计的局部多项式估计AI 解读

We study a multivariate regression discontinuity design in which treatment is assigned by crossing a boundary in the space of multiple running variables. We document that the existing bandwidth selector is suboptimal for a multivariate regression discontinuity design when the distance to a boundary point is used for its running variable, and introduce a multivariate local-linear estimator for multivariate regression discontinuity designs. Our estimator is asymptotically…