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多值处理下的回归不连续设计AI 解读

Summary We study identification and estimation in the regression discontinuity design with a multivalued treatment. We show that heterogeneity in the first stage discontinuities can be used for the identification of the marginal treatment effects under an alternative assumption, namely, the homogeneity of the LATEs along some covariates. This assumption can often be tested and relaxed. Our estimator can be programmed as a simple two‐stage least squares regression, and…

含整合或平稳噪声的多重水平突变检验AI 解读

Summary The paper analyzes the detection and estimation of multiple level shifts regardless of the order of integration of the time series. We show that it is possible to extend the Bai‐Perron methodology (1998) to the I(1) and NI(1) nonstationary cases so that a unified framework to test for the presence of multiple level shifts in a robust way is designed. The finite sample performance of the proposed statistics is carried out, establishing a comparison with other existing…

概率聚类的广义贝叶斯框架AI 解读

Summary Loss-based clustering methods, such as k-means clustering and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on mixture models provides an alternative approach, but such methods face computational problems and are highly sensitive to the choice of kernel. In this article we propose a generalized Bayes framework that bridges…

多元线性回归中的高维方差分析AI 解读

Summary In this paper, we develop a systematic theory for high-dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new U-type statistic to test linear hypotheses and establish a high-dimensional Gaussian approximation result under fairly mild moment assumptions. Our general framework and theory can be used to deal with the classical one-way multivariate…

中位数正则性与诚实推断AI 解读

Summary We introduce a new notion of regularity of an estimator called median regularity. We prove that uniformly valid honest inference for a functional is possible if and only if there exists a median regular estimator of that functional. To the best of our knowledge, such a notion of regularity that is necessary for uniformly valid inference is unavailable in the literature.

空间混杂的谱域调整AI 解读

Summary Adjusting for an unmeasured confounder is generally an intractable problem, but in the spatial setting it may be possible under certain conditions. We derive necessary conditions on the coherence between the exposure and the unmeasured confounder that ensure the effect of exposure is estimable. We specify our model and assumptions in the spectral domain to allow for different degrees of confounding at different spatial resolutions. One assumption that ensures…

基于参数 Copula 的依赖删失模型AI 解读

Summary Consider a survival time $T$ that is subject to random right censoring, and suppose that $T$ is stochastically dependent on the censoring time $C$. We are interested in the marginal distribution of $T$. This situation is often encountered in practice. Consider, for example, the case where $T$ is a patient’s time to death from a certain disease. Then the censoring time $C$ could be the time until the patient leaves the study or the time until death from another cause.…

二元结果概率预测的诚实校准评估AI 解读

Summary Probability predictions from binary regressions or machine learning methods ought to be calibrated: if an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the so-called calibration curve $p(\cdot)$ should equal the identity, i.e., $p(x) = x$ for all $x$ in the unit interval. We propose honest calibration assessment based on novel confidence bands for the calibration curve, which are valid…

群组效应异质性与干扰下的时变因果效应调节AI 解读

Summary The micro-randomized trial is a sequential randomized experimental design to empirically evaluate the effectiveness of mobile health intervention components that may be delivered at hundreds or thousands of decision points. Micro-randomized trials have motivated a new class of causal estimands, termed causal excursion effects, for which semiparametric inference can be conducted via a weighted, centred least-squares criterion (Boruvka et al., 2018). Causal excursion…

变量消除、图约简与有效 g 公式AI 解读

Summary We study efficient estimation of an interventional mean associated with a point exposure treatment under a causal graphical model represented by a directed acyclic graph without hidden variables. Under such a model, a subset of the variables may be uninformative, in that failure to measure them neither precludes identification of the interventional mean nor changes the semiparametric variance bound for regular estimators of it. We develop a set of graphical criteria…

利用阈值化 graphical lasso 处理潜变量AI 解读

Summary Structural learning of Gaussian graphical models in the presence of latent variables has long been a challenging problem. Chandrasekaran et al. (2012) proposed a convex program for estimating a sparse graph plus a low-rank term that adjusts for latent variables; however, this approach poses challenges from both computational and statistical perspectives. We propose an alternative, simple solution: apply a hard-thresholding operator to existing graph selection…

多元区间删失数据的边际比例风险模型AI 解读

Summary Multivariate interval-censored data arise when there are multiple types of events or clusters of study subjects, such that the event times are potentially correlated and when each event is only known to occur over a particular time interval. We formulate the effects of potentially time-varying covariates on the multivariate event times through marginal proportional hazards models while leaving the dependence structures of the related event times unspecified. We…

用于因果推断的线性回归隐含权重AI 解读

Summary A basic principle in the design of observational studies is to approximate the randomized experiment that would have been conducted under ideal circumstances. At present, linear regression models are commonly used to analyse observational data and estimate causal effects. How do linear regression adjustments in observational studies emulate key features of randomized experiments, such as covariate balance, self-weighted sampling and study representativeness? In this…

最大最小效应的统计推断：识别跨研究稳定关联AI 解读

Integrative analysis of data from multiple sources is critical to making generalizable discoveries. Associations consistently observed across multiple source populations are more likely to be generalized to target populations with possible distributional shifts. In this paper, we model the heterogeneous multi-source data with multiple high-dimensional regressions and make inferences for the maximin effect (Meinshausen, Bühlmann, AoS, 43(4), 1801–1830). The maximin effect…

因子增强逆回归及其微生物组数据分析应用AI 解读

We investigate the relationship between count data that inform the relative abundance of features of a composition, and factors that influence the composition. Our work is motivated from microbiome studies aiming to extract microbial signatures that are predictive of host phenotypes based on data collected from a group of individuals harboring radically different microbial communities. We introduce multinomial Factor Augmented Inverse Regression (FAIR) of the count vector…

稀疏网络中社区数量的估计AI 解读

Among the nonparametric methods of estimating the number of communities (K) in a community detection problem, methods based on the spectrum of the Bethe Hessian matrices (Hζ with the scalar parameter ζ) have garnered much popularity for their simplicity, computational efficiency, and robustness to the sparsity of data. For certain heuristic choices of ζ, such methods have been shown to be consistent for networks with N nodes with a common expected degree of ω( log N). In…

说服效应的识别AI 解读

This paper examines a commonly used measure of persuasion whose precise interpretation has been obscure in the literature. By using the potential outcome framework, we define the causal persuasion rate by a proper conditional probability of taking the action of interest with a persuasive message conditional on not taking the action without the message. We then formally study identification under empirically relevant data scenarios and show that the commonly adopted measure…

时变极值依赖结构的统计推断AI 解读

We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and of the spectral measures integrated over time. The uniform asymptotic normality of these estimators is proved under suitable nonparametric smoothness and regularity assumptions. We then use the process convergence of the integrated spectral…

高维正则化回归估计量的普适性AI 解读

The Convex Gaussian Min–Max Theorem (CGMT) has emerged as a prominent theoretical tool for analyzing the precise stochastic behavior of various statistical estimators in the so-called high-dimensional proportional regime, where the sample size and the signal dimension are of the same order. However, a well-recognized limitation of the existing CGMT machinery rests in its stringent requirement on the exact Gaussianity of the design matrix, therefore rendering the obtained…

离线强化学习中的投影状态—动作平衡权重AI 解读

Off-policy evaluation is considered a fundamental and challenging problem in reinforcement learning (RL). This paper focuses on value estimation of a target policy based on pre-collected data generated from a possibly different policy, under the framework of infinite-horizon Markov decision processes. Motivated by the recently developed marginal importance sampling method in RL and the covariate balancing idea in causal inference, we propose a novel estimator with…

凸约束下含噪线性逆问题的高维精确风险渐近AI 解读

In the standard Gaussian linear measurement model Y=Xμ0+ξ∈Rm with a fixed noise level σ>0, we consider the problem of estimating the unknown signal μ0 under a convex constraint μ0∈K, where K is a closed convex set in Rn. We show that the risk of the natural convex constrained least squares estimator (LSE) μˆ(σ) can be characterized exactly in high-dimensional limits, by that of the convex constrained LSE μˆKseq in the corresponding Gaussian sequence model at a different…

序贯可忽略性下部分可观测马尔可夫决策过程的离策略评估AI 解读

We consider off-policy evaluation of dynamic treatment rules under sequential ignorability, given an assumption that the underlying system can be modeled as a partially observed Markov decision process (POMDP). We propose an estimator, partial history importance weighting, and show that it can consistently estimate the stationary mean rewards of a target policy, given long enough draws from the behavior policy. We provide an upper bound on its error that decays polynomially…

信号去噪的交叉验证框架：趋势滤波、二分 CART 等应用AI 解读

This paper formulates a general cross-validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as trend filtering and dyadic CART. The resulting cross-validated versions are then shown to attain nearly the same rates of convergence as are known for the optimally tuned analogues. There did not exist any previous theoretical analyses of cross-validated versions of trend filtering or dyadic CART. To illustrate the…

偏差与方差权衡的下界AI 解读

It is a common phenomenon that for high-dimensional and nonparametric statistical models, rate-optimal estimators balance squared bias and variance. Although this balancing is widely observed, little is known whether methods exist that could avoid the trade-off between bias and variance. We propose a general strategy to obtain lower bounds on the variance of any estimator with bias smaller than a prespecified bound. This shows to which extent the bias-variance trade-off is…