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高维时间序列数据的序列相关与 ARCH 效应检验AI 解读

This article proposes several tests for detecting serial correlation and ARCH effect in high-dimensional data. The dimension of data p=p(n) may go to infinity when the sample size n→∞

数据丰富环境下的通胀预测：机器学习方法的益处AI 解读

Inflation forecasting is an important but difficult task. Here, we explore advances in machine learning (ML) methods and the availability of new datasets to forecast U.S. inflation. Despite the skepticism in the previous literature, we show that ML models with a large number of covariates are systematically more accurate than the benchmarks. The ML method that deserves more attention is the random forest model, which dominates all other models. Its good performance is due…

黑箱模型的因果解释AI 解读

The fields of machine learning and causal inference have developed many concepts, tools, and theory that are potentially useful for each other. Through exploring the possibility of extracting causal interpretations from black-box machine-trained models, we briefly review the languages and concepts in causal inference that may be interesting to machine learning researchers. We start with the curious observation that Friedman’s partial dependence plot has exactly the same…

含全局因子与组特定因子的因子模型收缩估计AI 解读

This article develops an adaptive group lasso estimator for factor models with both global and group-specific factors. The global factors can affect all variables, whereas the group-specific factors are only allowed to affect the variables within a certain group. We propose a new method to separately identify the spaces spanned by global and group-specific factors, and we develop a new shrinkage estimator that can consistently estimate the factor loadings and determine the…

大数据经济预测：稀疏性的幻象AI 解读

We compare sparse and dense representations of predictive models in macroeconomics, microeconomics, and finance. To deal with a large number of possible predictors, we specify a prior that allows for both variable selection and shrinkage. The posterior distribution does not typically concentrate on a single sparse model, but on a wide set of models that often include many predictors.

伪因子分析AI 解读

This paper draws parallels between the principal components analysis of factorless high‐dimensional nonstationary data and the classical spurious regression. We show that a few of the principal components of such data absorb nearly all the data variation. The corresponding scree plot suggests that the data contain a few factors, which is corroborated by the standard panel information criteria. Furthermore, the Dickey–Fuller tests of the unit root hypothesis applied to the…

分位数因子模型AI 解读

Quantile factor models (QFM) represent a new class of factor models for high‐dimensional panel data. Unlike approximate factor models (AFM), which only extract mean factors, QFM also allow unobserved factors to shift other relevant parts of the distributions of observables. We propose a quantile regression approach, labeled Quantile Factor Analysis (QFA), to consistently estimate all the quantile‐dependent factors and loadings. Their asymptotic distributions are established…

处理选择中的模型选择：惩罚化福利最大化AI 解读

This paper studies a penalized statistical decision rule for the treatment assignment problem. Consider the setting of a utilitarian policy maker who must use sample data to allocate a binary treatment to members of a population, based on their observable characteristics. We model this problem as a statistical decision problem where the policy maker must choose a subset of the covariate space to assign to treatment, out of a class of potential subsets. We focus on settings…

用于估计与推断的深度神经网络AI 解读

We study deep neural networks and their use in semiparametric inference. We establish novel nonasymptotic high probability bounds for deep feedforward neural nets. These deliver rates of convergence that are sufficiently fast (in some cases minimax optimal) to allow us to establish valid second‐step inference after first‐step estimation with deep learning, a result also new to the literature. Our nonasymptotic high probability bounds, and the subsequent semiparametric…

波动率的固定k推断AI 解读

We present a new theory for the conduct of nonparametric inference about the latent spot volatility of a semimartingale asset price process. In contrast to existing theories based on the asymptotic notion of an increasing number of observations in local estimation blocks, our theory treats the estimation block size k as fixed. While the resulting spot volatility estimator is no longer consistent, the new theory permits the construction of asymptotically valid and…

动态离散博弈估计中的均衡约束实施AI 解读

Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these restrictions have different merits and limitations. Algorithms that guarantee local convergence typically require the approximation of high‐dimensional Jacobians. Alternatively, the Nested Pseudo‐Likelihood (NPL) algorithm is a fixed‐point iterative procedure, which avoids the computation of these matrices, but—in games—may fail to…

用于大规模贝叶斯变量选择的扩展随机梯度 MCMCAI 解读

Summary Stochastic gradient Markov chain Monte Carlo algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed dimension and the log-posterior density is differentiable with respect to the parameters. This paper proposes an extended stochastic gradient Markov chain Monte Carlo algorithm which, by introducing appropriate latent variables, can be…

高维不平衡逻辑回归的高效后验抽样AI 解读

Summary Classification with high-dimensional data is of widespread interest and often involves dealing with imbalanced data. Bayesian classification approaches are hampered by the fact that current Markov chain Monte Carlo algorithms for posterior computation become inefficient as the number $p$ of predictors or the number $n$ of subjects to classify gets large, because of the increasing computational time per step and worsening mixing rates. One strategy is to employ a…

回归变量选择的新方法及其在遗传精细定位中的应用AI 解读

Summary We introduce a simple new approach to variable selection in linear regression, with a particular focus on quantifying uncertainty in which variables should be selected. The approach is based on a new model—the ‘sum of single effects’ model, called ‘SuSiE’—which comes from writing the sparse vector of regression coefficients as a sum of ‘single-effect’ vectors, each with one non-zero element. We also introduce a corresponding new fitting procedure—iterative Bayesian…

多维空间与图上的保序回归AI 解读

In this paper, we study minimax and adaptation rates in general isotonic regression. For uniform deterministic and random designs in $[0,1]^{d}$ with ${d\ge2}$ and $N(0,1)$ noise, the minimax rate for the $\ell_{2}$ risk is known to be bounded from below by $n^{-1/d}$ when the unknown mean function $f$ is nondecreasing and its range is bounded by a constant, while the least squares estimator (LSE) is known to nearly achieve the minimax rate up to a factor $(\log n)^{\gamma}$…

超越高斯近似：独立随机向量之和最大值的自助法AI 解读

The Bonferroni adjustment, or the union bound, is commonly used to study rate optimality properties of statistical methods in high-dimensional problems. However, in practice, the Bonferroni adjustment is overly conservative. The extreme value theory has been proven to provide more accurate multiplicity adjustments in a number of settings, but only on an ad hoc basis. Recently, Gaussian approximation has been used to justify bootstrap adjustments in large scale simultaneous…

通过位移凸性分析两层神经网络AI 解读

Fitting a function by using linear combinations of a large number $N$ of “simple” components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to kernel regression, to boosting. In general, the resulting risk minimization problem is nonconvex and is solved by gradient descent or its variants. Unfortunately, little is known about global convergence properties of these approaches. Here,…

高维协方差矩阵检验AI 解读

The paper introduces a new test for testing structures of covariances for high dimensional vectors and the data dimension can be much larger than the sample size. Under proper normalization, central and noncentral limit theorems are established. The asymptotic theory is attained without imposing any explicit restriction between data dimension and sample size. To facilitate the related statistical inference, we propose the balanced Rademacher weighted differencing scheme,…

模型选择与局部几何AI 解读

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases—including common classes of causal or graphical models, as well as time series models—distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: first, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than…

结构化、回归及在线场景中错误发现比例的同时高概率界AI 解读

While traditional multiple testing procedures prohibit adaptive analysis choices made by users, Goeman and Solari (Statist. Sci. 26 (2011) 584–597) proposed a simultaneous inference framework that allows users such flexibility while preserving high-probability bounds on the false discovery proportion (FDP) of the chosen set. In this paper, we propose a new class of such simultaneous FDP bounds, tailored for nested sequences of rejection sets. While most existing simultaneous…

通过投影平均构造稳健的多元非参数检验AI 解读

In this work, we generalize the Cramér–von Mises statistic via projection averaging to obtain a robust test for the multivariate two-sample problem. The proposed test is consistent against all fixed alternatives, robust to heavy-tailed data and minimax rate optimal against a certain class of alternatives. Our test statistic is completely free of tuning parameters and is computationally efficient even in high dimensions. When the dimension tends to infinity, the proposed test…

高维情形下基于距离与再生核希尔伯特空间的依赖度量AI 解读

In this paper, we study distance covariance, Hilbert–Schmidt covariance (aka Hilbert–Schmidt independence criterion [In Advances in Neural Information Processing Systems (2008) 585–592]) and related independence tests under the high dimensional scenario. We show that the sample distance/Hilbert–Schmidt covariance between two random vectors can be approximated by the sum of squared componentwise sample cross-covariances up to an asymptotically constant factor, which indicates…

回归中的经验贝叶斯预言机不确定性量化AI 解读

We propose an empirical Bayes method for high-dimensional linear regression models. Following an oracle approach that quantifies the error locally for each possible value of the parameter, we show that an empirical Bayes posterior contracts at the optimal rate at all parameters and leads to uniform size-optimal credible balls with guaranteed coverage under an “excessive bias restriction” condition. This condition gives rise to a new slicing of the entire space that is…

基于秩相关最大值的高维一致独立性检验AI 解读

Testing mutual independence for high-dimensional observations is a fundamental statistical challenge. Popular tests based on linear and simple rank correlations are known to be incapable of detecting nonlinear, nonmonotone relationships, calling for methods that can account for such dependences. To address this challenge, we propose a family of tests that are constructed using maxima of pairwise rank correlations that permit consistent assessment of pairwise independence.…