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Normality pre-tests on reduced-form innovations cannot detect whether two or more underlying structural shocks are Gaussian, and hence cannot detect a failure of identification in non-Gaussian SVARs. We propose a bootstrap-based approach that reveals such a failure. Under the null of valid identification and certain regularity conditions, the conditional bootstrap distribution of the maximum likelihood estimator of the impact matrix is asymptotically normal, so the…

预期高安慰剂反应时安慰剂对照随机试验的因果效应估计AI 解读

In placebo-controlled randomized clinical trials (RCTs), the placebo response significantly modifies treatment effects and diminishes the intention-to-treat (ITT) treatment effect, $Δ_{ITT}$. This study presents a novel two-stage framework for estimating the standardized causal treatment effect, $Δ_{STD}$, among the ITT population, under the assumption that their placebo responses are similar to the levels of self-administering medication at home. The first stage employs a…

Two frequent approaches for identifying structural VARs are external instruments, which carry economic content but are often weak, and non-Gaussianity of the shocks, which provides statistical identification but carries no economic meaning. We combine the two strategies in a single generalized method of moments framework. This hybrid approach point-identifies the target shocks while also identifying the non-target shocks up to sign and ordering. Under suitable rank…

This article introduces a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification. We begin with an ambiguity set - a frequentist model that pairs a possibly misspecified likelihood with every possible prior - and uniformly expand it by a Kullback-Leibler radius to accommodate likelihood misspecification. We show that optimal decisions under this framework are equivalent to minimax decisions with an exponentially tilted loss…

高维线性回归的统一谱分析：去偏与阈值化AI 解读

We use spectral analysis to establish a unified theory of debiasing, thresholding, and simultaneous inference for high-dimensional linear regression with ill-conditioned designs. The methods include Ridge regression, spectral cut-off, and iterative and dynamical regression procedures. A common debiasing procedure uses two applications of the original linear algorithm with fixed parameters. Spectral analysis shows that debiasing squares the residual, while implementations…

基于小球方法的物理信息统计学习复杂度相关误差率AI 解读

Physics-informed statistical learning (PISL) integrates empirical data with physical knowledge to enhance the statistical performance of estimators. While PISL methods are widely used in practice, a comprehensive theoretical understanding of how informed regularization affects statistical properties is still missing. Specifically, two fundamental questions have yet to be fully addressed: (A) what is the trade-off between soft penalties and hard constraints, and (B) what is…

凸正则化的谱依赖：右旋转不变设计下的基本极限AI 解读

We study the fundamental limits of convex-regularized estimation in high-dimensional linear regression with right-rotationally invariant design matrices. We show that the asymptotic risks of convex-penalized least squares estimators are lower bounded by the risk of an approximate message passing algorithm known as Bayes VAMP, and we further characterize when the lower bound is attainable. As a technical ingredient in the proof of our lower bound theorem, we characterize the…

RBF 核高斯过程最大似然估计的精确渐近理论AI 解读

Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the…

Joint-event forecasts combine an estimated dependence model with current marginal forecasts. Retaining historical transforms at the marginal fits available when each outcome arrived creates overlapping estimation errors. We derive their joint influence with the terminal estimates in a stable Vine Copula VAR with normal innovation margins and a fixed, correctly specified Gaussian or positive Clayton vine. An intercept identity and the stable VAR filter reduce the historical…

利用高频波动率检验爆炸性泡沫AI 解读

Based on a continuous-time stochastic volatility model with a linear drift, we develop a test for explosive behavior in financial asset prices at a low frequency when prices are sampled at a higher frequency. The test exploits the volatility information in the high-frequency data. The method consists of devolatizing log-asset price increments with realized volatility measures and performing a supremum-type recursive Dickey-Fuller test on the devolatized sample. The proposed…

Wigner 矩阵时间序列的相变监测AI 解读

We develop methodology and theory for the detection of a phase transition in a time-series of high-dimensional random matrices. In the model we study, at each time point \( t = 1,2,\ldots \), we observe a deformed Wigner matrix \( \mathbf{M}_t \), where the unobservable deformation represents a latent signal. This signal is detectable only in the supercritical regime, and our objective is to detect the transition to this regime in real time, as new matrix--valued…

Factor models for longitudinal data, where policy adoption is unconfounded with respect to a low-dimensional set of latent factor loadings, have become increasingly popular for causal inference. Most existing approaches, however, rely on a causal finite-sample approach or computationally intensive methods, limiting their applicability and external validity. In this paper, we propose a novel method for panel causal inference within a super-population framework, based on…

In this paper, we develop bootstrap methods for factor-augmented regressions with potentially weak common components, allowing signal eigenvalues to diverge at heterogeneous rates $N^{α_k}$, where $0<α_k\leq1$, $k=1,\ldots,r$. The regression estimator targets a rotation of the latent parameter vector that may be data dependent, while factor estimation can induce asymptotic bias. The proposed procedure directly constructs the rotation-specific target in the bootstrap world,…

We study structural changes in multivariate time series by estimating and comparing stationary graphs of macroeconomic time series before and after an economic crisis, such as the Great Recession. Building on a latent time series framework called Orthogonally-rotated Univariate Time-series (OUT), we propose a shared-parameter framework-the spOUT autoregressive model (spOUTAR)-that jointly models two related multivariate time series and enables coherent Bayesian estimation of…

We develop a semiparametric continuous time inferential framework for testing cumulative treatment effects, including both immediate and carryover effects. The latent state process is modeled by an ordinary differential equation (ODE) whose drift depends on state and treatment, while the observed data are noisy measurements of this latent state at irregular, multi resolution time points. We define the average treatment effect (ATE) as the difference of expected cumulative…

Under i.i.d. sampling, the maximum score estimator of Manski (1975) converges at the cube-root rate to a non-Gaussian limit. We show that, under multiway dependence and low-level conditions, it is asymptotically normal at a parametric rate in the smallest number of clusters and, when the cluster-level variance is non-degenerate, as fast as regular estimators such as probit. The result rests on a general theory for non-smooth M-estimators, under which a modified bootstrap is…

Governments and development partners often seek Sustainable Development Goal (SDG) "accelerators" whose progress can propagate gains across human well-being, institutions, resources, and environmental priorities. Such claims require evidence on direction, timing, robustness, and trade-offs, not only network connectivity. We map directed SDG interdependence using a balanced panel of 114 countries observed annually from 2000 to 2024. Because the goal series are persistent,…