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精度矩阵最小二乘：高维估计与推断AI 解读

The least squares estimator can be cast as depending only on the precision matrix of the data, similar to the weights of a global minimum variance portfolio. We give conditions under which any plug-in precision matrix estimator produces an unbiased and consistent least squares estimator for stationary time series regressions, in both low- and high-dimensional settings. Such conditions define a class of “Precision Least Squares” (PrLS) estimators, which are shown to be…

资产收益中因子强度的不稳定性AI 解读

We study the problem of detecting structural instability of factor strength in asset pricing models for financial returns with observable factors.We allow for strong and weaker factors, in which the sum of squared betas grows at a rate equal to and slower than the number of test assets, respectively: this growth rate determines the strength of the corresponding factor.We propose LM and Wald statistics for the null hypothesis of stability and derive their asymptotic…

观察性研究中多值处理政策学习的模型选择AI 解读

This study investigates the policy learning problem in observational studies, where the treatment variable can be multivalued and the propensity scores are unknown. We approximate the optimal policy in a global policy class with infinite complexity (VC/Natarajan) dimension, using a sequence of sieve policy classes with finite complexity dimension. The optimal policy within each sieve class is estimated by maximizing the empirical welfare, constructed through the doubly…

长期方差的正定收敛核估计AI 解读

Kernel estimators have been popular for decades in long-run variance estimation.To minimize the loss of efficiency measured by the mean-squared error in important aspects of kernel estimation, we propose a novel class of converging kernel estimators with three major properties: (a) the optimal bandwidth choice is model-free; (b) positive-definiteness is ensured through a principle-driven aggregation technique with no loss of theoretical efficiency; and (c) potentially…

去偏 Lasso 的小调参选择AI 解读

In this study, we investigate the bias and variance properties of the debiased Lasso in linear regression when the tuning parameter of the node-wise Lasso is selected to be smaller than in previous studies. We consider the case where the number of covariates p is bounded by a constant multiple of the sample size n. First, we show that the bias of the debiased Lasso can be reduced without diverging the asymptotic variance by setting the order of the tuning parameter to 1/n.…

生产者—消费者模型识别与推断的显示偏好方法AI 解读

This paper provides a new identification result for a large class of models in which consumers participate in production. I show that consumer preferences are necessary and sufficient to identify production functions through cross-equation restrictions implied by first-order conditions. In addition, I derive a nonparametric revealed preference characterization of the class of models that exhausts its empirical implications. Finally, I use a novel and easy-to-apply inference…

微观结构噪声下傅里叶瞬时波动率估计的渐近正态性与有限样本稳健性AI 解读

We study the efficiency and robustness of the Fourier spot volatility estimator when high-frequency prices are contaminated by microstructure noise. First, we show that the estimator is consistent and asymptotically efficient in the presence of additive noise, establishing a Central Limit Theorem (CLT) with the optimal rate of convergence n1/8. Additionally, we complete the asymptotic theory in the absence of noise, obtaining a CLT with the optimal rate of convergence n1/4.…

极端连续处理效应的估计与推断AI 解读

This article studies estimation and inference for the treatment effect in deep tails of the potential outcome distributions corresponding to a continuously valued treatment, namely the extreme continuous treatment effect. We consider two measures for the tail characteristics: the quantile function and the tail mean function defined as the conditional mean beyond a quantile level. Then, for a quantile level close to 1, we define the extreme quantile treatment effect (EQTE)…

裂区设计中的再随机化与协变量调整AI 解读

Split-plot designs are widely used in agricultural, industrial, social, and biomedical experiments to accommodate hard-to-change factors. Given multiple factors of interest and experimental units that are nested within groups, the design assigns a subset of the factors by a cluster randomization at the group level and assigns the remaining factors by a stratified randomization at the unit level. The randomization mechanism ensures covariate balance on average at both the…

状态空间模型的高效重要性变分近似AI 解读

Variational methods are a potentially scalable estimation approach for state space models.However, existing methods are inaccurate or computationally infeasible for many state space models.This article proposes a variational approximation that is accurate and fast for any model with a closed-form measurement density function and a state transition distribution within the exponential family of distributions.Our approach constructs a variational approximation to the states…

交叉验证后自助法选择高维 M 估计量的惩罚参数AI 解读

We develop a new method for selecting the penalty parameter for ℓ1-penalized M-estimators in high dimensions, which we refer to as bootstrapping after cross validation. We derive rates of convergence for the corresponding ℓ1-penalized M-estimator and also for the post-ℓ1-penalized M-estimator, which refits the nonzero entries of the former estimator without penalty in the criterion function. We demonstrate via simulations that our methods are not dominated by cross…

受配给约束的生育：子女数量—质量权衡中的处理效应异质性AI 解读

We develop a generalized theory of rationed fertility to analyze treatment effect heterogeneity in the child quantity-quality trade-off. An exogenous increase in fertility can be either desired or undesired. We derive a positive rationing income effect on child quality for desired fertility increases but a negative rationing income effect for undesired fertility increases. We propose an econometric framework to identify treatment effects of desired and undesired fertility…

函数值空间过程的谱密度估计AI 解读

The spectral density function describes the second-order properties of a stationary stochastic process on Rd. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process taking values in a separable Hilbert space. Our estimator is based on kernel smoothing and can be applied to a wide variety of spatial sampling schemes including those in which data are observed at irregular spatial locations. Thus, it finds immediate…

通过神经对抗不变性学习从异质环境中追寻因果关系AI 解读

Pursuing causality from data is a fundamental problem in scientific discovery, treatment intervention, and transfer learning. This paper introduces a novel algorithmic method for addressing nonparametric invariance and causality learning in regression models across multiple environments, where the joint distribution of response variables and covariates varies, but the conditional expectations of outcome given an unknown set of quasi-causal variables are invariant. The…

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基于样本协方差矩阵的完全随机缺失检验AI 解读

We study the problem of testing whether the missing values of a potentially high-dimensional dataset are Missing Completely at Random (MCAR). We relax the problem of testing MCAR to the problem of testing the compatibility of a collection of covariance matrices, motivated by the fact that this procedure is feasible when the dimension grows with the sample size. Our first contributions are to define a natural measure of the incompatibility of a collection of correlation…

鞅的 Yurinskii 耦合AI 解读

Yurinskii’s coupling is a popular theoretical tool for nonasymptotic distributional analysis in mathematical statistics and applied probability, offering a Gaussian strong approximation with an explicit error bound under easily verifiable conditions. Originally stated in ℓ2-norm for sums of independent random vectors, it has recently been extended both to the ℓp-norm, for 1≤p≤∞, and to vector-valued martingales in ℓ2-norm, under some strong conditions. We present as our main…

It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating expectations of functions in a given family, with uniform error bounds; this is closely related to the problem of estimating the mean of a random vector under a general norm. The second problem considered is that of regression with quadratic loss.…

强化学习中稳健策略评估的在线估计与推断AI 解读

Reinforcement learning has emerged as one of the prominent topics attracting attention in modern statistical learning, with policy evaluation being a key component. Unlike the traditional machine learning literature on this topic, our work emphasizes statistical inference for the model parameters and value functions of reinforcement learning algorithms. While most existing analyses assume random rewards to follow standard distributions, we embrace the concept of robust…

离散观测数据的函数主成分分析理论AI 解读

Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on eigen-decomposition plays a central role for data reduction and representation. After nearly three decades of research, there remains a key problem unsolved, namely, the perturbation analysis of covariance operator for diverging number of eigencomponents…

Plackett–Luce 模型中似然估计量的统一分析AI 解读

The Plackett–Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model’s likelihood. In this paper, we investigate the asymptotic theory of utility vector estimation by maximizing different types of likelihood, such as full, marginal, and quasi-likelihood. Starting from interpreting the estimating equations of these estimators to gain some…

对称性：非参数回归中的一般结构AI 解读

In this paper, we present the framework of symmetry in nonparametric regression. This generalises the framework of covariate sparsity, where the regression function f:[0,1]d→R depends only on at most s

高维广义线性模型的贝叶斯模型选择一致性进展AI 解读

Uncovering genuine relationships between a response variable and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian literature is well-developed and there are no substantial differences in the model selection consistency results available from the two schools. For generalized linear models (GLMs), however, Bayesian model selection consistency results are lacking in…

分布式强化学习中的估计与统计推断AI 解读

In this paper, we study distributional reinforcement learning from the perspective of statistical efficiency. We investigate distributional policy evaluation, aiming to estimate the complete return distribution (denoted $η^π$) attained by a given policy $π$. We use the certainty-equivalence method to construct our estimator $\hatη^π$, given a generative model is available. In this circumstance we need a dataset of size $\widetilde O\left(\frac{|\mathcal{S}||\mathcal{A}|}{\varepsilon^{2p}(1-γ)^{2p+2}}\right)$…

矩阵情境在线决策中的统计推断AI 解读

The study of online decision-making problems that leverage contextual information has drawn notable attention due to their significant applications in fields ranging from healthcare to autonomous systems. In modern applications, contextual information can be rich and is often represented as a matrix. Moreover, while existing online decision algorithms mainly focus on reward maximization, less attention has been devoted to statistical inference. To address these gaps, in this…