论文检索

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…

从高维含噪数据学习低维非线性结构：积分算子方法AI 解读

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from noisy and high-dimensional observations, where the data sets are assumed to be sampled from a nonlinear manifold model and corrupted by high-dimensional noise. The algorithm employs an adaptive bandwidth selection procedure which does not rely on prior knowledge of the underlying manifold. The obtained low-dimensional embeddings can be further utilized for downstream…

通过算法稳定性进行选择后推断AI 解读

When the target of statistical inference is chosen in a data-driven manner, the guarantees provided by classical theories vanish. We propose a solution to the problem of inference after selection by building on the framework of algorithmic stability, in particular its branch with origins in the field of differential privacy. Stability is achieved via randomization of selection and it serves as a quantitative measure that is sufficient to obtain nontrivial post-selection…

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…

持久贝蒂数及其他稳定化统计量的自助法AI 解读

We investigate multivariate bootstrap procedures for general stabilizing statistics, with specific application to topological data analysis. The work relates to other general results in the area of stabilizing statistics, including central limit theorems for geometric and topological functionals of Poisson and binomial processes in the critical regime, where limit theorems prove difficult to use in practice, motivating the use of a bootstrap approach. A smoothed bootstrap…

非平稳时间序列的图模型AI 解读

We propose NonStGM, a general nonparametric graphical modeling framework, for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian graphical models (GGM) and stationary time series graphical models (StGM) and complements existing works on parametric graphical models based on change point vector autoregressions (VAR). Analogous to StGM, the proposed framework captures conditional noncorrelations…

放宽独立同分布假设：通过平方根熵正则化实现自适应极小极大遗憾AI 解读

We consider prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. This semi-adversarial setting includes (at the extremes) the classical i.i.d. setting, when the unknown constraint set is restricted to be a singleton, and the unconstrained adversarial setting, when the constraint set is the set of all distributions. The Hedge algorithm—long known to be minimax (rate) optimal in the adversarial…

单指标 Fréchet 回归AI 解读

Single index models provide an effective dimension reduction tool in regression, especially for high-dimensional data, by projecting a general multivariate predictor onto a direction vector. We propose a novel single-index model for regression models where metric space-valued random object responses are coupled with multivariate Euclidean predictors. The responses in this regression model include complex, non-Euclidean data, including covariance matrices, graph Laplacians of…

连接因子模型与稀疏模型AI 解读

Factor and sparse models are widely used to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a supervised learning methodology that allows for efficiently exploring all the information in high-dimensional datasets. The method is based on a flexible model for high-dimensional panel data with observable and/or latent common factors and idiosyncratic…

最优变点检测与定位AI 解读

Given a times series Y in Rn, with a piecewise constant mean and independent components, the twin problems of change-point detection and change-point localization, respectively amount to detecting the existence of times where the mean varies and estimating the positions of those change-points. In this work, we tightly characterize optimal rates for both problems and uncover the phase transition phenomenon from a global testing problem to a local estimation problem.…

含协变量的尾指数估计：股票收益尾部风险动态AI 解读

This paper provides novel theoretical results for the estimation of the conditional tail index of Pareto and Pareto-type distributions in a time series context. We show that both the estimators and relevant test statistics are normally distributed in the limit, when independent and identically distributed or dependent data are considered. Simulation results provide support for the theoretical findings and highlight the good finite sample properties of the approach in a time…

总量需求随机系数 Logit 模型的半非参数估计AI 解读

In this paper, we propose a two-step semi-nonparametric estimator for the widely used random coefficients logit demand model. The approach applies to the same setup as Berry et al. (1995, BLP)-type of models with many products, but has the advantage of not requiring computing demand inversion. In particular, the first step of our approach estimates the fixed coefficients via a computationally very easy linear sieve generalized method of moments (GMM). The second step…

非线性局部非平稳滤波器的随机性质AI 解读

This article delivers conditions for the existence of a unique stationary, ergodic and φ-mixing invertible solution for nonlinear time-varying parameter models that are locally non-stationary or explosive. The assumptions are different from existing conditions as they do not impose Lipschitz, bounded growth or drift restrictions. Instead we require that the time series contains resetting dynamics. These dynamics are present in time series with sudden changes, such as stock…

非可分三角模型中个体处理效应的推断AI 解读

In nonseparable triangular models with a binary endogenous treatment and a binary instrumental variable, Vuong and Xu (2017) established identification results for individual treatment effects (ITEs) under the rank invariance assumption. Using their approach, Feng et al. (2019) proposed a uniformly consistent kernel estimator for the density of the ITE that utilizes estimated ITEs. In this paper, we establish the asymptotic normality of the density estimator of Feng et al.…

稀疏分位数回归AI 解读

We consider both ℓ0-penalized and ℓ0-constrained quantile regression estimators. For the ℓ0-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and apply it to obtain non-asymptotic upper bounds on the mean-square parameter and regression function estimation errors. We also derive analogous results for the ℓ0-constrained estimator. The resulting rates of convergence are nearly minimax-optimal and the same as…

含群组效应的高效同伴效应估计AI 解读

We study linear peer effect models where peers interact in groups and individual’s outcomes are linear in the group mean outcome and characteristics. We allow for unobserved random group effects as well as observed fixed group effects. The specification is in part motivated by the moment conditions imposed in Graham (2008). We show that these moment conditions can be cast in terms of a linear random group effects model and that they lead to a class of GMM estimators with…

双重差分的新进展：近期计量文献的综合梳理AI 解读

This paper synthesizes recent advances in the econometrics of difference-in-differences (DiD) and provides concrete recommendations for practitioners. We begin by articulating a simple set of “canonical” assumptions under which the econometrics of DiD are well-understood. We then argue that recent advances in DiD methods can be broadly classified as relaxing some components of the canonical DiD setup, with a focus on (i) multiple periods and variation in treatment timing,…

社会互动阈值回归AI 解读

This paper develops a threshold social interaction model which introduces group-specific endogenous effects as well as contextual effects into a conventional spatial Durbin model. We propose a two-step GMM estimator for the threshold and regression parameters, derive asymptotic theory, and provide bootstrap inference. Finally, we assess the performance of our methods using a Monte Carlo simulation and provide an empirical application on the role of peer effects on student…

线性回归中适当聚类层级的检验AI 解读

The overwhelming majority of empirical research that uses cluster-robust inference assumes that the clustering structure is known, even though there are often several possible ways in which a dataset could be clustered. We propose two tests for the correct level of clustering in regression models. One test focuses on inference about a single coefficient, and the other on inference about two or more coefficients. We provide both asymptotic and wild bootstrap implementations.…