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This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we rederive known unbiased estimators of expectations with respect to the stationary distribution of a Markov chain and provide conditions for the finiteness of their moments. We further construct unbiased estimators of the asymptotic variance of Markov chain ergodic…

利用双重机器学习估计平均偏效应AI 解读

Single-parameter summaries of variable effects in regression settings are desirable for ease of interpretation. However, (partially) linear models, for example, which would deliver these, may fit poorly to the data. On the other hand, an interpretable summary of the contribution of a given predictor is provided by the so-called average partial effect—the average slope of the regression function with respect to the predictor of interest. Although one can construct a doubly…

泊松经验贝叶斯估计：何时先验建模优于边际建模？AI 解读

Empirical Bayes (EB) is a popular framework for large-scale inference that aims to find data-driven estimators to compete with the Bayesian oracle that knows the true prior. Two principled approaches to EB estimation have emerged over the years: f-modeling, which constructs an approximate Bayes rule by estimating the marginal distribution of the data, and g-modeling, which estimates the prior from data and then applies the learned Bayes rule. For the Poisson model, the…

流式数据下函数线性回归的可扩展推断AI 解读

Traditional static functional data analysis is facing new challenges due to streaming data, where data constantly flows in. A major challenge is that storing such an ever-increasing amount of data in memory is nearly infeasible. In addition, existing inferential tools in online learning are mainly developed for finite-dimensional problems, while inference methods for functional data are focused on the offline settings. In this paper, we focus on the online estimation of…

The matrix normal model, that is, the family of Gaussian matrix-variate distributions whose covariance matrices are the Kronecker product of two lower-dimensional factors, is frequently used to model matrix-variate data. The tensor normal model generalizes this family to Kronecker products of three or more factors. We study the estimation of the Kronecker factors of the covariance matrix in the matrix and tensor normal models. For the above models, we show that the maximum…

依赖边随机图中参数维数增长的伪似然 M 估计AI 解读

An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We demonstrate that scalable estimation of random graph models with dependent edges is possible, by establishing convergence rates of pseudo-likelihood-based M-estimators for discrete undirected graphical models with exponential parameterizations…

切片逆回归的结构维度问题AI 解读

In this work, we address the longstanding puzzle that Sliced Inverse Regression (SIR) often performs poorly for sufficient dimension reduction when the structural dimension d (the dimension of the central space) exceeds 4. We first show that in the multiple index model Y=f(PX)+ϵ where X is a p-standard normal vector, ϵ is an independent noise, and P is a projection operator from Rp to Rd, if the link function f follows the law of a Gaussian process. Then with high…

泛函估计中 Le Cam 方法的对偶化Ⅰ：一般理论AI 解读

Le Cam’s method (or the two-point method) is a commonly used tool for obtaining statistical lower bound and especially popular for functional estimation problems. This work aims to explain and give conditions for the tightness of Le Cam’s lower bound in functional estimation from the perspective of convex duality. Under a variety of settings, it is shown that the maximization problem that searches for the best two-point lower bound, upon dualizing, becomes a minimization…

高频金融数据的大型瞬时波动率矩阵非参数估计AI 解读

In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalized shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot…

风险价值与期望损失联合回归的最优模型平均AI 解读

Since the implementation of the Basel III Accord, expected shortfall (ES) has gained increasing attention from regulators as a complement to value-at-risk (VaR). The problem of elicitability for ES makes jointly modeling VaR and ES a popular method to study ES. In this article, we develop model averaging for joint VaR and ES regression models that selects the two weight vectors by minimizing a jackknife criterion. We show the large sample properties of the estimators under…

非平稳时间序列非线性泛函的一般极限理论AI 解读

New limit theory is provided for a wide class of sample variance and covariance functionals involving both nonstationary and stationary time series. Sample functionals of this type commonly appear in regression applications and the asymptotics are particularly relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root, or fractional processes. The limit theory is unusually general in that it covers both parametric and…

未观测个体异质性极端分位数的推断AI 解读

We develop a methodology for conducting inference on extreme quantiles of unobserved individual heterogeneity (e.g., heterogeneous coefficients and treatment effects) in panel data and meta-analysis settings. Inference is challenging in such settings: only noisy estimates of heterogeneity are available, and central limit approximations perform poorly in the tails. We derive a necessary and sufficient condition under which noisy estimates are informative about extreme…

聚类相依下的稳健工具变量推断AI 解读

Summary Linear instrumental variables (IV) models with clustering dependence are widely used in empirical studies, although the common solution, the cluster covariance estimator, often produces undesirable inferential results, especially with weak instruments. In this paper, I propose a method that is robust to both weak IV and (potentially heterogeneous) clustering dependence. The proposed method is based on the idea of Fama–MacBeth estimation, with group-level estimators…

利用正则化后分布回归评估最低工资的分布效应AI 解读

Summary We evaluate the distributional effects of a minimum wage introduction based on a dataset with a moderate sample size, but a large number of potential covariates. In this context, the selection of relevant control variables at each distributional threshold is crucial to test hypotheses about the impact of the continuous treatment variable. To this end, we use a post-double-selection logistic distribution regression approach, which allows for uniformly valid inference…

固定效应静态面板模型的双重机器学习AI 解读

Summary Recent advances in causal inference have seen the development of methods that make use of the predictive power of machine learning algorithms. In this paper, we develop novel double machine learning procedures for panel data in which these algorithms are used to approximate high-dimensional and non-linear nuisance functions of the covariates. Our new procedures are extensions of the well-known correlated random effects, within-group, and first-difference estimators…

存在内生性时 probit 与 tobit 模型的边际效应AI 解读

Summary 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 non-linear models. We study this issue, focusing on the instrumental variable (IV) probit and tobit models. We show that even when a valid instrumental variable is available, failing to differentiate between the two types of endogeneity can lead to…

局部投影的统计推断AI 解读

Summary Inference for impulse responses estimated with local projections presents interesting challenges and opportunities. Analysts typically want to assess the precision of individual estimates, explore the dynamic evolution of the response over particular regions, and generally determine whether the impulse generates a response that is any different from the null of no effect. Each of these goals requires a different approach to inference. In this article, we provide an…

主成分分析能否保留因子载荷的稀疏性？AI 解读

This article studies the principal component analysis (PCA) estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PCA estimators of loadings, which comes from the approximately (block) upper triangular structure of the rotation matrix. It suggests an asymmetric relationship among factors: the sparsity of the rotated loadings for a stronger factor can be contaminated by the loadings from weaker ones, but the…

基因与环境交互作用的经济学与计量方法AI 解读

Abstract We discuss how to estimate the interplay between genes (nature) and environments (nurture), with an empirical illustration of the moderating effect of school starting age on one’s genetic predisposition towards educational attainment. We argue that gene–environment (G×E) studies can be instrumental for (i) assessing treatment effect heterogeneity, (ii) testing theoretical predictions, and (iii) uncovering mechanisms, thereby improving understanding of how (policy)…

风险厌恶竞标者与选择性进入下第一价格拍卖的识别与推断AI 解读

Abstract We study identification and inference in first-price auctions with risk-averse bidders and selective entry, building on a flexible framework we call the Affiliated Signal with Risk Aversion (AS-RA) model. Assuming exogenous variation in either the number of potential bidders (N) or a continuous instrument (z) shifting opportunity costs of entry, we provide a sharp characterization of the nonparametric restrictions implied by equilibrium bidding. This…

Abstract I partially identify the marginal treatment effect (MTE) when the treatment is misclassified. I explore two restrictions, allowing for dependence between the instrument and the misclassification decision. If the signs of the propensity scores’ derivatives are equal, I identify the MTE sign. If those derivatives are similar, I bound the MTE. To illustrate, I analyze the impact of alternative sentences (fines and community service versus no punishment) on recidivism…

面板数据中的缓慢变动个体AI 解读

Panel data often contain stayers and slow movers . The literature proposes an estimator for the average partial effects (APEs) for this setting without a formal theory. The literature is also silent about inference in the presence of stayers and many slow movers. We contribute to this state of the art. First, we develop an asymptotic theory to guarantee that such an estimator is consistent in the presence of stayers and slow movers. Second, we propose its standard error.…

通过因果表征学习构建可解释的深度生成模型AI 解读

Recent developments in generative artificial intelligence (AI) rely on machine learning techniques such as deep learning and generative modeling to achieve state-of-the-art performance across wide-ranging domains. These methods’ surprising performance is due in part to their ability to learn implicit “representations” of complex, multi-modal data. Unfortunately, deep neural networks are notoriously black boxes that obscure these representations, making them difficult to…

可能性推断模型：综述AI 解读

An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher’s fiducial argument have similar objectives, but a fundamental distinction between the two is that the former doesn’t require that uncertainty quantification be probabilistic, offering greater flexibility and allowing for a proof of its reliability. Important recent developments have been made…