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基于偏 Gini 协方差的重尾误差高维线性模型稳健推断AI 解读

This paper introduces a novel robust high-dimensional inference framework based on partial Gini covariance. We specifically address the practically important problem of quantifying how changes in features affect the conditional mean in high-dimensional linear regression when the random noises are heavy-tailed and possibly asymmetric. Conventional high-dimensional regression inference methods suffer from inaccurate type I errors and reduced power in heavy-tailed contexts.…

强化学习中的分布型离策略评估AI 解读

In the literature of reinforcement learning (RL), off-policy evaluation is mainly focused on estimating a value of a target policy given the pre-collected data generated by some behavior policy. Motivated by the recent success of distributional RL in many practical applications, we study the distributional off-policy evaluation problem in the batch setting when the reward is multi-variate. We propose an offline Wasserstein-based approach to simultaneously estimate the joint…

双重非同质环境中的离策略评估AI 解读

This work aims to study off-policy evaluation (OPE) under scenarios where two key reinforcement learning (RL) assumptions -- temporal stationarity and individual homogeneity are both violated. To handle the ``double inhomogeneities", we propose a class of latent factor models for the reward and observation transition functions, under which we develop a general OPE framework that consists of both model-based and model-free approaches. To our knowledge, this is the first paper…

连续处理效应的非参数双重稳健检验AI 解读

The vast majority of literature on evaluating the significance of a treatment effect based on observational data has been confined to discrete treatments. These methods are not applicable to drawing inference for a continuous treatment, which arises in many important applications. To adjust for confounders when evaluating a continuous treatment, existing inference methods often rely on discretizing the treatment or using (possibly misspecified) parametric models for the…

高维正则化分位数回归全局与局部最优解的次梯度分析AI 解读

Regularized quantile regression (QR) is a useful technique for analyzing heterogeneous data under potentially heavy-tailed error contamination in high dimensions. This paper provides a new analysis of the estimation/prediction error bounds of the global solution of $L_1$ -regularized QR (QR-LASSO) and the local solutions of nonconvex regularized QR (QR-NCP) when the number of covariates is greater than the sample size. Our results build upon and significantly generalize the…

事件时间结局下最优个体化决策规则的变换不变学习AI 解读

In many important applications of precision medicine, the outcome of interest is time to an event (e.g., death, relapse of disease) and the primary goal is to identify the optimal individualized decision rule (IDR) to prolong survival time. Existing work in this area have been mostly focused on estimating the optimal IDR to maximize the restricted mean survival time in the population. We propose a new robust framework for estimating an optimal static or dynamic IDR with…

面向公平性的最优个体化处理规则学习AI 解读

There has recently been a surge on the methodological development for optimal individualized treatment rule (ITR) estimation. The standard methods in the literature are designed to maximize the potential average performance (assuming larger outcomes are desirable). A notable drawback of the standard approach, due to heterogeneity in treatment response, is that the estimated optimal ITR may be suboptimal or even detrimental to certain disadvantaged subpopulations. Motivated…

高维最优治疗规则的模型辅助一致诚实推断AI 解读

This article develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate simultaneous inference to determine if a group of variables is relevant for estimating an optimal decision rule in a high-dimensional semiparametric framework. The unknown link function permits flexible modeling of the interactions…

高维分位数回归：卷积平滑与凹正则化AI 解读

Abstract ℓ 1 -penalized quantile regression (QR) is widely used for analysing high-dimensional data with heterogeneity. It is now recognized that the ℓ1-penalty introduces non-negligible estimation bias, while a proper use of concave regularization may lead to estimators with refined convergence rates and oracle properties as the signal strengthens. Although folded concave penalized M-estimation with strongly convex loss functions have been well studied, the extant…

高维回归中免手工调参的稳健高效方法AI 解读

We introduce a novel approach for high-dimensional regression with theoretical guarantees. The new procedure overcomes the challenge of tuning parameter selection of Lasso and possesses several appealing properties. It uses an easily simulated tuning parameter that automatically adapts to both the unknown random error distribution and the correlation structure of the design matrix. It is robust with substantial efficiency gain for heavy-tailed random errors while maintaining…

双重切片辅助的高维删失数据充分降维AI 解读

This paper provides a unified framework and an efficient algorithm for analyzing high-dimensional survival data under weak modeling assumptions. In particular, it imposes neither parametric distributional assumption nor linear regression assumption. It only assumes that the survival time $T$ depends on a high-dimensional covariate vector $\mathbf{X}$ through low-dimensional linear combinations of covariates $\Gamma ^{T}\mathbf{X}$. The censoring time is allowed to be…

异方差误差下惩罚分位数回归的野生残差自助推断AI 解读

We consider a heteroscedastic regression model in which some of the regression coefficients are zero but it is not known which ones. Penalized quantile regression is a useful approach for analysing such data. By allowing different covariates to be relevant for modelling conditional quantile functions at different quantile levels, it provides a more complete picture of the conditional distribution of a response variable than mean regression. Existing work on penalized…

分位数最优治疗规则AI 解读

Finding the optimal treatment regime (or a series of sequential treatment regimes) based on individual characteristics has important applications in areas such as precision medicine, government policies and active labor market interventions. In the current literature, the optimal treatment regime is usually defined as the one that maximizes the average benefit in the potential population. This paper studies a general framework for estimating the quantile-optimal treatment…

偏倚抽样下生存数据分位数回归的估计与推断AI 解读

Biased sampling occurs frequently in economics, epidemiology, and medical studies either by design or due to data collecting mechanism. Failing to take into account the sampling bias usually leads to incorrect inference. We propose a unified estimation procedure and a computationally fast resampling method to make statistical inference for quantile regression with survival data under general biased sampling schemes, including but not limited to the length-biased sampling,…

超高维部分线性可加分位数回归AI 解读

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete picture of the conditional distribution of a response variable given high dimensional covariates. (2) The sparsity level is allowed to be different at different quantile levels. (3) The partially linear additive structure accommodates…

中等高维支持向量机的变量选择AI 解读

Summary The support vector machine (SVM) is a powerful binary classification tool with high accuracy and great flexibility. It has achieved great success, but its performance can be seriously impaired if many redundant covariates are included. Some efforts have been devoted to studying variable selection for SVMs, but asymptotic properties, such as variable selection consistency, are largely unknown when the number of predictors diverges to ∞. We establish a unified theory…

高维均值向量的非参数多元检验AI 解读

This work is concerned with testing the population mean vector of nonnormal high-dimensional multivariate data. Several tests for high-dimensional mean vector, based on modifying the classical Hotelling T2 test, have been proposed in the literature. Despite their usefulness, they tend to have unsatisfactory power performance for heavy-tailed multivariate data, which frequently arise in genomics and quantitative finance. This article proposes a novel high-dimensional…

超高维非凸惩罚回归的校准AI 解读

We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is…

高维异质数据的分位数自适应无模型变量筛选AI 解读

We introduce a quantile-adaptive framework for nonlinear variable screening with high-dimensional heterogeneous data. This framework has two distinctive features: (1) it allows the set of active variables to vary across quantiles, thus making it more flexible to accommodate heterogeneity; (2) it is model-free and avoids the difficult task of specifying the form of a statistical model in a high dimensional space. Our nonlinear independence screening procedure employs spline…

用于分析超高维异质性的分位数回归AI 解读

Ultra-high dimensional data often display heterogeneity due to either heteroscedastic variance or other forms of non-location-scale covariate effects. To accommodate heterogeneity, we advocate a more general interpretation of sparsity which assumes that only a small number of covariates influence the conditional distribution of the response variable given all candidate covariates; however, the sets of relevant covariates may differ when we consider different segments of the…

协变量数量发散时聚类二元数据的 GEE 分析AI 解读

Clustered binary data with a large number of covariates have become increasingly common in many scientific disciplines. This paper develops an asymptotic theory for generalized estimating equations (GEE) analysis of clustered binary data when the number of covariates grows to infinity with the number of clusters. In this “large n, diverging p” framework, we provide appropriate regularity conditions and establish the existence, consistency and asymptotic normality of the GEE…

变系数模型的局部秩推断AI 解读

By allowing the regression coefficients to change with certain covariates, the class of varying coefficient models offers a flexible approach to modeling nonlinearity and interactions between covariates. This paper proposes a novel estimation procedure for the varying coefficient models based on local ranks. The new procedure provides a highly efficient and robust alternative to the local linear least squares method, and can be conveniently implemented using existing R…

局部加权删失分位数回归AI 解读

Censored quantile regression offers a valuable supplement to Cox proportional hazards model for survival analysis. Existing work in the literature often requires stringent assumptions, such as unconditional independence of the survival time and the censoring variable or global linearity at all quantile levels. Moreover, some of the work uses recursive algorithms, making it challenging to derive asymptotic normality. To overcome these drawbacks, we propose a new locally…

估计方程框架下纵向数据的一致模型选择与数据驱动光滑检验AI 解读

Summary Model selection for marginal regression analysis of longitudinal data is challenging owing to the presence of correlation and the difficulty of specifying the full likelihood, particularly for correlated categorical data. The paper introduces a novel Bayesian information criterion type model selection procedure based on the quadratic inference function, which does not require the full likelihood or quasi-likelihood. With probability approaching 1, the criterion…