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高维线性回归中大量零约束的检验AI 解读

We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with k ≫ n regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension regression models with nuisance terms. The parsimoniously parameterized models identify whether the original parameter of interest is or is not zero. Estimating fixed low dimension sub-parameters ensures greater estimator accuracy, it does not require…

用马尔可夫转换因子模型刻画高维数据AI 解读

We study a novel large dimensional approximate factor model with regime changes in the loadings driven by a latent first order Markov process. By exploiting the equivalent linear representation of the model, we first recover the latent factors by means of Principal Component Analysis. We then cast the model in state–space form, and we estimate loadings and transition probabilities through an EM algorithm based on a modified version of the Baum–Lindgren–Hamilton–Kim filter…

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异质性处理效应机器学习推断评论：序贯验证方法AI 解读

We use the martingale construction of Luedtke and van der Laan (2016) to develop tests for the presence of treatment heterogeneity. The resulting sequential validation approach can be instantiated using various validation metrics, such as BLPs, GATES, QINI curves, etc., and provides an alternative to cross‐validation‐like cross‐fold application of these metrics. This note was prepared as a comment on the Fisher–Schultz paper by Chernozhukov, Demirer, Duflo, and…

异质性处理效应机器学习推断评论：随机化推断方法AI 解读

We examine the split‐sample robust inference (SSRI) methodology introduced by Chernozhukov, Demirer, Duflo, and Fernandez‐Val for quantifying uncertainty in heterogeneous treatment effect estimates produced by machine learning (ML) models. Although SSRI properly accounts for the additional variability due to sample splitting, its computational cost becomes prohibitive with complex ML models. We propose an alternative approach based on randomization inference (RI) that…

随机实验中异质性处理效应的通用机器学习推断及印度免疫接种应用AI 解读

We propose strategies to estimate and make inference on key features of heterogeneous effects in randomized experiments. These key features include best linear predictors of the effects using machine learning proxies, average effects sorted by impact groups , and average characteristics of most and least impacted units . The approach is valid in high‐dimensional settings, where the effects are proxied (but not necessarily consistently estimated) by predictive and causal…

交互固定效应高维面板模型的估计与推断AI 解读

We develop new econometric methods for estimation and inference in high‐dimensional panel data models with interactive fixed effects. Our approach can be regarded as a nontrivial extension of the very popular common correlated effects (CCE) approach. Roughly speaking, we proceed as follows: We first construct a projection device to eliminate the unobserved factors from the model by applying a dimensionality reduction transform to the matrix of cross‐sectionally averaged…

高斯图模型估计中的若干算法AI 解读

Abstract In Gaussian graphical models, the likelihood equations must typically be solved iteratively. This paper investigates two algorithms: a version of iterative proportional scaling, which avoids inversion of large matrices, and an algorithm based on convex duality and operating on the covariance matrix by neighbourhood coordinate descent, which corresponds to the graphical lasso with zero penalty. For large, sparse graphs, the iterative proportional scaling algorithm…

含非多项式维干扰参数的可能误设广义线性模型推断AI 解读

Summary It is routine practice in statistical modelling to first select variables and then make inference for the selected model as in stepwise regression. Such inference is made upon the assumption that the selected model is true. However, without this assumption, one would not know the validity of the inference. Similar problems also exist in high-dimensional regression with regularization. To address these problems, we propose a dimension-reduced generalized likelihood…

高维生存数据最优治疗策略的无模型变量筛选AI 解读

Summary We propose a model-free variable screening method for the optimal treatment regime with high-dimensional survival data. The proposed screening method provides a unified framework to select the active variables in a prespecified target population, including the treated group as a special case. Based on this framework, the optimal treatment regime is exactly the optimal classifier that minimizes a weighted misclassification error rate, with weights associated with…

不受维度限制的岭回归AI 解读

Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows proportionally to the number of rows of the data matrix. This is not always the most natural setting in statistics where columns correspond to covariates and rows to samples. With the objective to move beyond the proportional asymptotics, we…

Testing the significance of a variable or group of variables X for predicting a response Y, given additional covariates Z, is a ubiquitous task in statistics. A simple but common approach is to specify a linear model, and then test whether the regression coefficient for X is nonzero. However, when the model is misspecified, the test may have poor power, for example, when X is involved in complex interactions, or lead to many false rejections. In this work, we study the…

维度增长的非参数交互模型中的深度神经网络AI 解读

Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the literature. However, most of the studies require the input dimension to be fixed and consequently ignore the effect of dimension on the rate of convergence and hamper their applications to modern big data with high dimensionality. In this paper,…

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基于球极投影的马尔可夫链蒙特卡洛AI 解读

High-dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves results in empirically observed “stickiness” and poor theoretical mixing properties—lack of geometric ergodicity. In this paper, we introduce a new class of MCMC samplers that map the original high-dimensional problem in Euclidean space onto a sphere and…

含交互固定效应的核范数正则化分位数回归AI 解读

This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of) interactive fixed effects. It also allows the number of covariates to grow slowly with N and T . We derive an error…

Vladimir Vovk 对《安全检验》的讨论意见AI 解读

The main result of this paper (Theorem 1) is elegant and satisfying, but in this comment I will concentrate on one of its limitations, namely the condition infW0D(Q‖PW0)<∞⁠. (Analogous conditions are present in all generalizations given in the paper.) Even in the toy binary case with an infinite horizon, this condition is typically violated. Consider, e.g., the case of Markov alternative hypotheses Q considered in Ramdas et al. (2022): a nonIID Markov probability measure (or…

Dey、Martin 与 Williams 对《安全检验》的讨论贡献AI 解读

Congratulations to Grünwald, de Heide, and Koolen (GHK) for their contribution to the exciting and rapidly growing literature on safe/anytime-valid inference. GHK’s proposal focused on problems in which a statistical model is available that determines the quantity of interest—the model parameter—and provides a likelihood function that drives the e-value construction. When data are observed and analysed sequentially, however, the data analyst typically cannot say with any…

相关性调整的去偏 Lasso：协变量模型不准确时的去偏AI 解读

Abstract We consider the problem of estimating a low-dimensional parameter in high-dimensional linear regression. Constructing an approximately unbiased estimate of the parameter of interest is a crucial step towards performing statistical inference. Several authors suggest to orthogonalize both the variable of interest and the outcome with respect to the nuisance variables, and then regress the residual outcome with respect to the residual variable. This is possible if the…

神经网络与随机森林的融合AI 解读

Abstract Neural networks and random forests are popular and promising tools for machine learning. This article explores the proper integration of these two approaches for nonparametric regression to improve the performance of a single approach. Specifically, we propose a neural network estimator with local enhancement provided by random forests. It naturally synthesizes the local relation adaptivity of random forests and the strong global approximation ability of neural…

动态张量的 CP 因子模型AI 解读

Abstract Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CANDECOMP/PARAFAC (CP) decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly…

分组数据部分线性模型中提高估计精度的夹心提升法AI 解读

Abstract We study partially linear models in settings where observations are arranged in independent groups but may exhibit within-group dependence. Existing approaches estimate linear model parameters through weighted least squares, with optimal weights (given by the inverse covariance of the response, conditional on the covariates) typically estimated by maximizing a (restricted) likelihood from random effects modelling or by using generalized estimating equations. We…

未观测混杂下处理效应的模型辅助敏感性分析：正则化校准估计AI 解读

Abstract Consider sensitivity analysis for estimating average treatment effects under unmeasured confounding, assumed to satisfy a marginal sensitivity model. At the population level, we provide new representations for the sharp population bounds and doubly robust estimating functions. We also derive new, relaxed population bounds, depending on weighted linear outcome quantile regression. At the sample level, we develop new methods and theory for obtaining not only doubly…

广播式非参数张量回归AI 解读

Abstract We propose a novel use of a broadcasting operation, which distributes univariate functions to all entries of the tensor covariate, to model the nonlinearity in tensor regression nonparametrically. A penalized estimation and the corresponding algorithm are proposed. Our theoretical investigation, which allows the dimensions of the tensor covariate to diverge, indicates that the proposed estimation yields a desirable convergence rate. We also provide a minimax lower…

参数不稳定下高维线性回归的变量选择AI 解读

This paper considers the problem of variable selection allowing for parameter instability. It distinguishes between signal and pseudo-signal variables that are correlated with the target variable, and noise variables that are not, and investigate the asymptotic properties of the One Covariate at a Time Multiple Testing (OCMT) method proposed by Chudik et al. (2018) under parameter insatiability. It is established that OCMT continues to asymptotically select an approximating…