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滚动验证下的在线估计：流式数据的自适应非参数估计AI 解读

Online nonparametric estimators are gaining popularity due to their efficient computation and competitive generalization abilities. An important example includes variants of stochastic gradient descent. These algorithms often take one sample point at a time and incrementally update the parameter estimate of interest. In this work, we consider model selection/hyperparameter tuning for such online algorithms. We propose a weighted rolling validation procedure, an online…

希尔伯特流形变量的高维Hilbert–Schmidt线性回归AI 解读

In this paper, we propose a novel high-dimensional linear regression technique for variables taking values in Hilbert manifolds. Our approach offers a flexible framework where the response and covariates originate from distinct spaces and are interconnected by Hilbert–Schmidt operators. Our methodology is designed for situations where the number of the covariates grows exponentially fast as the sample size increases and some of the covariates together with the response take…

动态网络的双重异质性模型AI 解读

Analysis of networks that evolve dynamically requires the joint modelling of individual snapshots and time dynamics. This paper proposes a new flexible two-way heterogeneity model towards this goal. The new model equips each node of the network with two heterogeneity parameters, one to characterize the propensity to form ties with other nodes statically and the other to differentiate the tendency to retain existing ties over time. With n observed networks each having p…

核岭回归的几何分析及其应用AI 解读

We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all nonnegative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the Multiple Descents problem, unifying the proofs of (In Proceedings of Thirty Third Conference on Learning Theory (2020) 2683–2711 PMLR) and (Ann. Statist. 49 (2021) 1029–1054) for polynomial kernels in nonasymptotic regime and we establish Multiple…

基于峰度的矩阵数据投影寻踪AI 解读

We develop projection pursuit for data that admit a natural representation in matrix form. For projection indices, we propose extensions of the classical kurtosis and Mardia's multivariate kurtosis. The first index estimates projections for both sides of the matrices simultaneously, while the second index finds the two projections separately. Both indices are shown to recover the optimally separating projection for two-group Gaussian mixtures in the full absence of any label…

灵活应对赢家诅咒的推断方法AI 解读

Across science and policy, decision-makers often need to draw conclusions about the best candidate among competing alternatives. For instance, researchers may seek to infer the effectiveness of the most successful treatment or determine which demographic group benefits most from a specific treatment. Similarly, in machine learning, practitioners are often interested in the population performance of the model that performs best empirically. However, cherry-picking the best…

网络干扰下基于平均场方法的因果效应估计AI 解读

We study causal effect estimation from observational data under interference. The interference pattern is captured by an observed network. We adopt the chain graph framework of (J. Amer. Statist. Assoc. 116 (2021) 833–844), which allows (i) interaction among the outcomes of distinct study units connected along the graph and (ii) long range interference, whereby the outcome of an unit may depend on the treatments assigned to distant units connected along the interference…

非参数隐马尔可夫与独立同分布模型中的聚类风险AI 解读

We conduct an in-depth analysis of the Bayes risk of clustering in the context of hidden Markov and i.i.d. models. In both settings, we identify the situations where this risk is comparable to the Bayes risk of classification and those where its minimizer, the Bayes clusterer, can be derived from the Bayes classifier. While we demonstrate that clustering based on the Bayes classifier does not always match the optimal Bayes clusterer, we show that this difference is primarily…

序贯实验中的反事实推断AI 解读

We consider after-study statistical inference for sequentially designed experiments wherein multiple units are assigned treatments for multiple time points using treatment policies that adapt over time. Our goal is to provide inference guarantees for the counterfactual mean at the smallest possible scale—mean outcome under different treatments for each unit and each time—with minimal assumptions on the adaptive treatment policy. Without any structural assumptions on the…

分位数回归的渐近精确选择后推断AI 解读

In modern data analysis, it is common to select a model before performing statistical inference. Selective inference tools make adjustments for the model selection process in order to ensure reliable inference post selection. In this paper, we introduce an asymptotic pivot to infer about the effects of selected variables on conditional quantile functions. Utilizing estimators from smoothed quantile regression, our proposed pivot is easy to compute and yields…

自适应线性回归中的近最优推断AI 解读

When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality can lead to erroneous results. We propose a family of online debiasing estimators to correct these distributional anomalies in least squares estimation. Our proposed methods take advantage of the covariance structure present in the…

通过协变量调整消除因果目标选择偏差的共同原因原则AI 解读

Average treatment effects (ATEs) may be subject to selection bias when they are estimated among only a nonrepresentative subset of the target population. Selection bias can sometimes be eliminated by conditioning on a “sufficient adjustment set” of covariates, even for some forms of missingness not at random (MNAR). Without requiring full specification of the causal structure, we consider sufficient adjustment sets to allow nonparametric identification of conditional ATEs in…

异质处理效应与异方差下的模型平均估计AI 解读

The primary focus of this article is to capture heterogeneous treatment effects measured by the conditional average treatment effect. A model averaging estimation scheme is proposed with multiple candidate linear regression models under heteroskedastic errors, and the properties of this scheme are explored analytically. First, it is shown that our proposal is asymptotically optimal in the sense of achieving the lowest possible squared error. Second, the convergence of the…

完备性是否必要？未识别线性模型中的估计AI 解读

Modern data analysis depends increasingly on estimating models via flexible high-dimensional or nonparametric machine learning methods, where the identification of structural parameters is often challenging and untestable. In linear settings, this identification hinges on the completeness condition, which requires the nonsingularity of a high-dimensional matrix or operator and may fail for finite samples or even at the population level. Regularized estimators provide a…

可能包含大量协变量的断点回归设计AI 解读

This article examines high-dimensional covariates in regression discontinuity design (RDD) analysis. We introduce estimation and inference methods for the RDD models that incorporate covariate selection while maintaining stability across various numbers of covariates. The proposed methods combine a localization approach using kernel weights with $\ell _{1}$ -penalization to handle high-dimensional covariates. We provide both theoretical and numerical evidence demonstrating…

利用观测结构信息估计全球金融市场的大规模波动矩阵AI 解读

In this article, we develop a novel large volatility matrix estimation procedure for analyzing global financial markets. Practitioners often use lower-frequency data, such as weekly or monthly returns, to address the issue of different trading hours in the international financial market. However, this approach can lead to inefficiency due to information loss. To mitigate this problem, our proposed method, called Structured Principal Orthogonal complEment Thresholding…

函数型工具变量回归及移民对本土工资影响的估计AI 解读

Functional linear regression has gained popularity as a statistical tool for studying the relationship between function-valued variables. However, in practice, it is hard to expect that the explanatory variables of interest are strictly exogenous, due to, for example, the presence of omitted variables and measurement error. This issue of endogeneity remains insufficiently explored, in spite of its empirical importance. To fill this gap, this article proposes new consistent…

无条件异方差下温和爆炸性自回归模型的推断AI 解读

Mildly explosive autoregressions have been extensively employed in recent theoretical and applied econometric work to model the phenomenon of asset market bubbles. An important issue in this context concerns the construction of confidence intervals for the autoregressive parameter that represents the degree of explosiveness. Existing studies rely on intervals that are justified only under conditional homoskedasticity/heteroskedasticity. This paper studies the problem of…

单调样本流失下的有效估计AI 解读

Attrition is monotonic when agents leaving multi-period studies do not return. Under a general missing at random (MAR) assumption, we study efficiency in estimation of parameters defined by moment restrictions on the distributions of the counterfactuals that were unrealized due to monotonic attrition. We discuss novel issues related to overidentification, usability of sample units, and the information content of various MAR assumptions for estimation of such parameters. We…

有序结果中内生变量效应的估计AI 解读

Abstract We examine the use of instrumental variable (IV) methods to measure the effect of a ceteris paribus change in an endogenous variable on an ordered outcome. Specifically, we use these methods to investigate the effect of neighborhood characteristics on subjective well-being (SWB) among participants in the Moving to Opportunity (MTO) housing voucher experiment. We find that the estimated positive effect of a decrease in neighborhood poverty on SWB is sensitive to the…

保序倾向得分匹配AI 解读

We propose a one-to-many matching estimator of the average treatment effect based on propensity scores estimated by isotonic regression. This approach is predicated on the assumption of monotonicity in the propensity score function, a condition that can be justified in many economic applications. We show that the nature of the isotonic estimator can help us to fix many problems of existing matching methods, including efficiency, choice of the number of matches, choice of…

通过子群格估计回归函数的最大对称性AI 解读

Abstract We present a method for estimating the maximal symmetry of a continuous regression function. Knowledge of such a symmetry can be used to significantly improve modelling by removing the modes of variation resulting from the symmetries. Symmetry estimation is carried out using hypothesis testing for invariance strategically over the subgroup lattice of a search group G acting on the feature space. We show that the estimation of the unique largest invariant subgroup of…

离散观测函数集合的常微分方程模型AI 解读

Abstract The exploration of dynamic systems governed by ordinary differential equations (ODEs) holds great interest in the field of statistics. Existing research mainly focuses on a single function. This study generalizes the scope to analyse a collection of functions observed at discretized times, with sampling frequencies varying from sparse to dense designs. The range of ODE models studied caters to diverse dynamic systems, and includes the complex nonlinear and…

数值型成对比较数据的最小二乘估计AI 解读

Abstract Least square estimators for graphical models for cardinal paired comparison data with and without covariates are rigorously analysed. Novel, graph-based, necessary, and sufficient conditions that guarantee strong consistency, asymptotic normality, and the exponential convergence of the estimated ranks are emphasized. A complete theory for models with covariates is laid out. In particular, conditions under which covariates can be safely omitted from the model are…