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带变量选择的多阶段平稳处理策略的渐近推断AI 解读

Dynamic treatment regimes or policies are a sequence of decision functions over multiple stages that are tailored to individual features. One important class of treatment policies in practice, namely multi-stage stationary treatment policies, prescribes treatment assignment probabilities using the same decision function across stages, where the decision is based on the same set of features consisting of time-evolving variables (e.g., routinely collected disease biomarkers).…

模型能用多久？选择大型预测模型重拟合时机的决策理论方法AI 解读

Large-scale prediction models using tools from artificial intelligence (AI) or machine learning (ML) are increasingly common across a variety of industries and scientific domains. Despite their effectiveness, training AI and ML tools at scale can cost tens or hundreds of thousands of dollars (or more); and even after a model is trained, substantial resources must be invested to keep models up-to-date. This paper presents a decision-theoretic framework for deciding when to…

半参数回归中双重机器学习的双重稳健推断AI 解读

Due to concerns about parametric model misspecification, there is interest in using machine learning to adjust for confounding when evaluating the causal effect of an exposure on an outcome. Unfortunately, exposure effect estimators that rely on machine learning predictions are generally subject to so-called plug-in bias, which can render naive $p$-values and confidence intervals invalid. Progress has been made via proposals like targeted minimum loss estimation and more…

带协变量的伯努利试验中处理分配的最优相关结构AI 解读

Given covariates for $n$ units, each of which is to receive a treatment with probability $1/2$, we study the question of how best to correlate their treatment assignments to minimize the variance of the IPW estimator of the average treatment effect. Past work by \cite{bai2022} found that the optimal stratified experiment is a matched-pair design, where the matching depends on oracle knowledge of the distributions of potential outcomes given covariates. We study the strictly…

基于高斯过程先验的非线性结构化潜因子模型贝叶斯分析AI 解读

Factor analysis models are widely utilized in social and behavioral sciences, such as psychology, education, and marketing, to measure unobservable latent traits. In this article, we introduce a nonlinear structured latent factor analysis model which is more flexible to characterize the relationship between manifest variables and latent factors. The confirmatory identifiability of the latent factor is discussed, ensuring the substantive interpretation of the latent factors.…

具有经验学习机制的非平稳非线性群组面板最小二乘估计AI 解读

We discuss techniques of estimation and inference for nonstationary nonlinear cohort panels with learning from experience, showing, inter alia, the consistency and asymptotic normality of the nonlinear least squares estimator used in empirical practice. Potential pitfalls for hypothesis testing are identified and solutions proposed. Monte Carlo simulations verify the properties of the estimator and corresponding test statistics in finite samples, while an application to a…

股票市场 Benford 定律与市场有效性的联系：一项实证研究AI 解读

Benford's law, or the law of the first significant digit, has been subjected to numerous studies due to its unique applications in financial fields, especially accounting and auditing. However, studies that addressed the law's establishment in the stock markets generally concluded that stock prices do not comply with the underlying distribution. The present research, emphasizing data randomness as the underlying assumption of Benford's law, has conducted an empirical…

增强 Lee 界的稳健性并收紧区间：随机单调性与对称性下的样本选择模型AI 解读

In the presence of sample selection, Lee's (2009) nonparametric bounds are a popular tool for estimating a treatment effect. However, the Lee bounds rely on the monotonicity assumption, whose empirical validity is sometimes unclear. Furthermore, the bounds are often regarded to be wide and less informative even under monotonicity. To address these issues, this study introduces a stochastic version of the monotonicity assumption alongside a nonparametric distributional shape…

重新审视硬阈值追踪：全自适应与锐利估计AI 解读

Hard Thresholding Pursuit (HTP) has aroused increasing attention for its robust theoretical guarantees and impressive numerical performance in non-convex optimization. In this paper, we introduce a novel tuning-free procedure, named Full-Adaptive HTP (FAHTP), that simultaneously adapts to both the unknown sparsity and signal strength of the underlying model. We provide an in-depth analysis of the iterative thresholding dynamics of FAHTP, offering refined theoretical…

含潜在因子的单指数模型高维推断AI 解读

Models with latent factors recently attract a lot of attention. However, most investigations focus on linear regression models and thus cannot capture nonlinearity. To address this issue, we propose a novel Factor Augmented Single-Index Model. We first address the concern whether it is necessary to consider the augmented part by introducing a score-type test statistic. Compared with previous test statistics, our proposed test statistic does not need to estimate the…

结构化函数因子增广下的稀疏学习AI 解读

As one of the most powerful tools for examining the association between functional covariates and a response, the functional regression model has been widely adopted in various interdisciplinary studies. Usually, a limited number of functional covariates are assumed in a functional linear regression model. Nevertheless, correlations may exist between functional covariates in high-dimensional functional linear regression models, which brings significant statistical challenges…

高维高斯图模型的拟合优度检验：基于可交换抽样AI 解读

We introduce a general framework for testing goodness-of-fit for Gaussian graphical models in both the low- and high-dimensional settings. This framework is based on a novel algorithm for generating exchangeable copies by conditioning on sufficient statistics. This framework provides exact finite-sample error control regardless of the dimension and allows flexible choices of test statistics to improve power. We explore several candidate test statistics and conduct extensive…

股票投资组合的 Copula 中心不对称性AI 解读

Financial crises are usually associated with increased cross-sectional dependence between asset returns, causing asymmetry between the lower and upper tail of return distribution. The detection of asymmetric dependence is now understood to be essential for market supervision, risk management, and portfolio allocation. I propose a non-parametric test procedure for the hypothesis of copula central symmetry based on the Cramér-von Mises distance of the empirical copula and its…

含共同随机趋势与多因子误差结构的矩阵时间序列推断AI 解读

We develop an estimation methodology for a factor model for high-dimensional matrix-valued time series, where common stochastic trends and common stationary factors can be present. We study, in particular, the estimation of (row and column) loading spaces, of the common stochastic trends and of the common stationary factors, and the row and column ranks thereof. In a set of (negative) preliminary results, we show that a projection-based technique fails to improve the rates…

多变量连续处理的效应异质性与重要性度量AI 解读

Estimating the joint effect of a multivariate, continuous exposure is crucial, particularly in environmental health where interest lies in simultaneously evaluating the impact of multiple environmental pollutants on health. We develop novel methodology that addresses two key issues for estimation of treatment effects of multivariate, continuous exposures. We use nonparametric Bayesian methodology that is flexible to ensure our approach can capture a wide range of data…

存在内生性时 Probit 与 Tobit 模型的边际效应AI 解读

When evaluating partial effects, it is important to distinguish between structural endogeneity and measurement errors. In contrast to linear models, these two sources of endogeneity affect partial effects differently in nonlinear models. We study this issue focusing on the Instrumental Variable (IV) Probit and Tobit models. We show that even when a valid IV is available, failing to differentiate between the two types of endogeneity can lead to either under- or…

借助辅助数据识别断点回归设计中的平均因果效应AI 解读

Regression discontinuity designs are widely used when treatment assignment is determined by whether a running variable exceeds a predefined threshold. However, most research focuses on estimating local causal effects at the threshold, leaving the challenge of identifying treatment effects away from the cutoff largely unaddressed. The primary difficulty in this context is that the treatment assignment is deterministically defined by the running variable, violating the…

高维线性模型的稀疏化同时置信区间AI 解读

Statistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to account for. A critical question remains unsettled; that is, is it possible and how to embed the inference of the model into the simultaneous inference of the coefficients? To this end, we propose a notion of simultaneous confidence intervals called the sparsified simultaneous confidence intervals. Our intervals…

基于匹配的政策学习AI 解读

The beneficial effects of treatments vary across individuals in most studies. Treatment heterogeneity motivates practitioners to search for the optimal policy based on personal characteristics. A long-standing common practice in policy learning has been estimating and maximizing the value function using weighting techniques. Matching is widely used in many applied disciplines to infer causal effects, which is intuitively appealing because the observed covariates are directly…

正则化M估计量的导数与残差分布及其自适应调参应用AI 解读

This paper studies M-estimators with gradient-Lipschitz loss function regularized with convex penalty in linear models with Gaussian design matrix and arbitrary noise distribution. A practical example is the robust M-estimator constructed with the Huber loss and the Elastic-Net penalty and the noise distribution has heavy-tails. Our main contributions are three-fold. (i) We provide general formulae for the derivatives of regularized M-estimators $\hatβ(y,X)$ where…

凸非可微正则项诱导的低维模式：渐近分布与模式恢复AI 解读

Popular regularizers with non-differentiable penalties, such as Lasso, Elastic Net, Generalized Lasso, or SLOPE, reduce the dimension of the parameter space by inducing sparsity or clustering in the estimators' coordinates. In this paper, we focus on linear regression and explore the asymptotic distributions of the resulting low-dimensional patterns when the number of regressors $p$ is fixed, the number of observations $n$ goes to infinity, and the penalty function increases…

基于组内重抽样的高维纵向数据惩罚拟似然AI 解读

The generalized estimating equation (GEE) method is a popular tool for longitudinal data analysis. However, GEE produces biased estimates when the outcome of interest is associated with cluster size, a phenomenon known as informative cluster size (ICS). In this study, we address this issue by formulating the impact of ICS and proposing an integrated approach to mitigate its effects. Our method combines the concept of within-cluster resampling with a penalized…

离策略学习中状态变量选择的图方法AI 解读

Sequential decision problems are widely studied across many areas of science. A key challenge when learning policies from historical data - a practice commonly referred to as off-policy learning - is how to ``identify'' the impact of a policy of interest when the observed data are not randomized. Off-policy learning has mainly been studied in two settings: dynamic treatment regimes (DTRs), where the focus is on controlling confounding in medical problems with short decision…

长期剂量反应曲线的核方法AI 解读

A core challenge in causal inference is how to extrapolate long term effects, of possibly continuous actions, from short term experimental data. It arises in artificial intelligence: the long term consequences of continuous actions may be of interest, yet only short term rewards may be collected in exploration. For this estimand, called the long term dose response curve, we propose a simple nonparametric estimator based on kernel ridge regression. By embedding the…