论文检索

大协方差矩阵的二次优化偏差AI 解读

We describe a puzzle involving the interactions between an optimization of a multivariate quadratic function and a "plug-in" estimator of a spiked covariance matrix. When the largest eigenvalues (i.e., the spikes) diverge with the dimension, the gap between the true and the out-of-sample optima typically also diverges. We show how to "fine-tune" the plug-in estimator in a precise way to avoid this outcome. Central to our description is a "quadratic optimization bias"…

无需稀疏性假设的高维协变量局部投影推断AI 解读

This paper presents a comprehensive local projections (LP) framework for estimating future responses to current shocks, robust to high-dimensional controls without relying on sparsity assumptions. The approach is applicable to various settings, including impulse response analysis and difference-in-differences (DiD) estimation. While methods like LASSO exist, they often assume most parameters are exactly zero, limiting their effectiveness in dense data generation processes. I…

高维协方差矩阵惩罚似然估计的统一方法AI 解读

We consider the problem of estimation of a covariance matrix for Gaussian data in a high dimensional setting. Existing approaches include maximum likelihood estimation under a pre-specified sparsity pattern, l_1-penalized loglikelihood optimization and ridge regularization of the sample covariance. We show that these three approaches can be addressed in an unified way, by considering the constrained optimization of an objective function that involves two suitably defined…

基于条件矩方法的异质性处理效应估计AI 解读

We propose a new estimator for heterogeneous treatment effects in a partially linear model (PLM) with multiple exogenous covariates and a potentially endogenous treatment variable. Our approach integrates a Robinson transformation to handle the nonparametric component, the Smooth Minimum Distance (SMD) method to leverage conditional mean independence restrictions, and a Neyman-Orthogonalized first-order condition (FOC). By employing regularized model selection techniques…

稳定的降秩向量自回归模型识别AI 解读

The vector autoregression (VAR) has been widely used in system identification, econometrics, natural science, and many other areas. However, when the state dimension becomes large the parameter dimension explodes. So rank reduced modelling is attractive and is well developed. But a fundamental requirement in almost all applications is stability of the fitted model. And this has not been addressed in the rank reduced case. Here, we develop, for the first time, a closed-form…

工具变量：非渐近视角AI 解读

We provide a non-asymptotic analysis of the linear instrumental variable estimator allowing for the presence of exogeneous covariates. In addition, we introduce a novel measure of the strength of an instrument that can be used to derive non-asymptotic confidence intervals. For strong instruments, these non-asymptotic intervals match the asymptotic ones exactly up to higher order corrections; for weaker instruments, our intervals involve adaptive adjustments to the instrument…

通过数据依赖粗化缩小逆倾向得分加权估计的置信区间AI 解读

Inverse propensity-score weighted (IPW) estimators are prevalent in causal inference for estimating average treatment effects in observational studies. Under unconfoundedness, given accurate propensity scores and $n$ samples, the size of confidence intervals of IPW estimators scales down with $n$, and, several of their variants improve the rate of scaling. However, neither IPW estimators nor their variants are robust to inaccuracies: even if a single covariate has an $\varepsilon>0$…

成对比较模型的可处理岭回归AI 解读

Paired comparison models, such as Bradley-Terry and Thurstone-Mosteller, are commonly used to estimate relative strengths of pairwise compared items in tournament-style data. We discuss estimation of paired comparison models with a ridge penalty. A new approach is derived which combines empirical Bayes and composite likelihoods without any need to re-fit the model, as a convenient alternative to cross-validation of the ridge tuning parameter. Simulation studies demonstrate…

条件矩阵变元 t 分布的 EM 估计AI 解读

Conditional matrix variate student $t$ distribution was introduced by Battulga (2024a). In this paper, we propose a new version of the conditional matrix variate student $t$ distribution. The paper provides EM algorithms, which estimate parameters of the conditional matrix variate student $t$ distributions, including general cases and special cases with Minnesota prior.

高维缺失数据下的逻辑回归：插补、正则化与普适性AI 解读

We study high-dimensional, ridge-regularized logistic regression in a setting in which the covariates may be missing or corrupted by additive noise. When both the covariates and the additive corruptions are independent and normally distributed, we provide exact characterizations of both the prediction error as well as the estimation error. Moreover, we show that these characterizations are universal: as long as the entries of the data matrix satisfy a set of independence and…

用于非对称贝叶斯小波收缩的一类先验AI 解读

This paper proposes a class of asymmetric priors to perform Bayesian wavelet shrinkage in the standard nonparametric regression model with Gaussian error. The priors are composed by mixtures of a point mass function at zero and one of the following distributions: asymmetric beta, Kumaraswamy, asymmetric triangular or skew normal. Statistical properties of the associated shrinkage rules such as squared bias, variance and risks are obtained numerically and discussed. Monte…

整群随机试验的共形因果推断：无需渐近近似的模型稳健方法AI 解读

Traditional statistical inference in cluster randomized trials typically invokes the asymptotic theory that requires the number of clusters to approach infinity. In this article, we propose an alternative conformal causal inference framework for analyzing cluster randomized trials that achieves the target inferential goal in finite samples without the need for asymptotic approximations. Different from traditional inference focusing on estimating the average treatment effect,…

数据驱动的随机投影与高维广义线性模型筛选AI 解读

We address the challenge of correlated predictors in high-dimensional GLMs, where regression coefficients range from sparse to dense, by proposing a data-driven random projection method. This is particularly relevant for applications where the number of predictors is (much) larger than the number of observations and the underlying structure -- whether sparse or dense -- is unknown. We achieve this by using ridge-type estimates for variable screening and random projection to…

干扰条件下异质性处理效应的非参数检验AI 解读

Statistical inference of heterogeneous treatment effects (HTEs) across predefined subgroups is challenging when units interact because treatment effects may vary by pre-treatment variables, post-treatment exposure variables (that measure the exposure to other units' treatment statuses), or both. Thus, the conventional HTEs testing procedures may be invalid under interference. In this paper, I develop statistical methods to infer HTEs and disentangle the drivers of treatment…

Cox 比例风险模型中未测混杂的非参数贝叶斯调整AI 解读

In observational studies, unmeasured confounders present a crucial challenge in accurately estimating desired causal effects. To calculate the hazard ratio (HR) in Cox proportional hazard models for time-to-event outcomes, two-stage residual inclusion and limited information maximum likelihood are typically employed. However, these methods are known to entail difficulty in terms of potential bias of HR estimates and parameter identification. This study introduces a novel…

函数型空间自回归模型AI 解读

This study introduces a novel spatial autoregressive model in which the dependent variable is a function that may exhibit functional autocorrelation with the outcome functions of nearby units. This model can be characterized as a simultaneous integral equation system, which, in general, does not necessarily have a unique solution. For this issue, we provide a simple condition on the magnitude of the spatial interaction to ensure the uniqueness in data realization. For…

连接最大后验估计与后验期望的匹配先验对AI 解读

Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We derive an asymptotic condition for a pair of prior densities under which the posterior mean based on one prior coincides with the MAP estimate based on the other prior. A sufficient condition for the existence of this prior pair relates to $α$-…

何时能够对弱潜在因子开展统计推断？AI 解读

This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal factor strength relative to the noise level or signal-to-noise ratio. Our theory is applicable regardless of the relative growth rate between the cross-sectional dimension $N$ and temporal dimension $T$. This more realistic assumption and…

适用于重复截面数据的合成双重差分AI 解读

The synthetic difference-in-differences method provides an efficient method to estimate a causal effect with a latent factor model. However, it relies on the use of panel data. This paper presents an adaptation of the synthetic difference-in-differences method for repeated cross-sectional data. The treatment is considered to be at the group level so that it is possible to aggregate data by group to compute the two types of synthetic difference-in-differences weights on these…

缺乏真实图时利用马尔可夫条件与最少边数选择有向无环图模型AI 解读

We give a novel nonparametric pointwise consistent statistical test (the Markov Checker) of the Markov condition for directed acyclic graph (DAG) or completed partially directed acyclic graph (CPDAG) models given a dataset. We also introduce the Cross-Algorithm Frugality Search (CAFS) for rejecting DAG models that either do not pass the Markov Checker test or that are not edge minimal. Edge minimality has been used previously by Raskutti and Uhler as a nonparametric…

最小稀疏性下含高维干扰函数的根号样本量一致半参数学习AI 解读

Treatment effect estimation under unconfoundedness is a fundamental task in causal inference. In response to the challenge of analyzing high-dimensional datasets collected in substantive fields such as epidemiology, genetics, economics, and social sciences, various methods for treatment effect estimation with high-dimensional nuisance parameters (the outcome regression and the propensity score) have been developed in recent years. However, it is still unclear what is the…

多元时间序列均值变点的检测AI 解读

This work delves into presenting a probabilistic method for analyzing linear process data with weakly dependent innovations, focusing on detecting change-points in the mean and estimating its spectral density. We develop a test for identifying change-points in the mean of data coming from such a model, aiming to detect shifts in the underlying distribution. Additionally, we propose a consistent estimator for the spectral density of the data, contingent upon fundamental…

众数因子分析：面向条件众数的高维降维方法AI 解读

The modal factor model represents a new factor model for dimension reduction in high dimensional panel data. Unlike the approximate factor model that targets for the mean factors, it captures factors that influence the conditional mode of the distribution of the observables. Statistical inference is developed with the aid of mode estimation, where the modal factors and the loadings are estimated through maximizing a kernel-type objective function. An easy-to-implement…

匹配式因果效应估计中的倾向得分增广AI 解读

When assessing the causal effect of a binary exposure using observational data, confounder imbalance across exposure arms must be addressed. Matching methods, including propensity score-based matching, can be used to deconfound the causal relationship of interest. They have been particularly popular in practice, at least in part due to their simplicity and interpretability. However, these methods can suffer from low statistical efficiency compared to many competing methods.…