论文检索

高维资产条件时变因子模型中的 Alpha 检验AI 解读

For conditional time-varying factor models with high-dimensional assets, this article proposes a high-dimensional alpha (HDA) test to assess whether there exist abnormal returns on securities (or portfolios) over the theoretical expected returns. To employ this test effectively, a constant coefficient test is also introduced. It examines the validity of constant alphas and factor loadings. Simulation studies and an empirical example are presented to illustrate the finite…

使用估计因子检验即时预测的单调性AI 解读

This article proposes a test to determine whether “big data” nowcasting methods, which have become an important tool to many public and private institutions, are monotonically improving as new information becomes available. The test is the first to formalize existing evaluation procedures from the nowcasting literature. We place particular emphasis on models involving estimated factors, since factor-based methods are a leading case in the high-dimensional empirical…

随机对照试验的最优数据收集AI 解读

Summary In a randomized control trial, the precision of an average treatment effect estimator and the power of the corresponding t-test can be improved either by collecting data on additional individuals, or by collecting additional covariates that predict the outcome variable. To design the experiment, a researcher needs to solve this trade-off subject to her budget constraint. We show that this optimization problem is equivalent to optimally predicting outcomes by the…

高维气候模型的统计近似AI 解读

We propose a general emulation method for constructing low-dimensional approximations of complex dynamic climate models. Our method uses artificially designed uncorrelated CO2 emissions scenarios, which are much better suited for the construction of an emulator than are conventional emissions scenarios. We apply our method to the climate model MAGICC to approximate the impact of emissions on global temperature. Comparing the temperature forecasts of MAGICC and our emulator,…

This paper proposes a valid bootstrap‐based distributional approximation for M ‐estimators exhibiting a Chernoff (1964)‐type limiting distribution. For estimators of this kind, the standard nonparametric bootstrap is inconsistent. The method proposed herein is based on the nonparametric bootstrap, but restores consistency by altering the shape of the criterion function defining the estimator whose distribution we seek to approximate. This modification leads to a generic and…

This paper analyzes a procedure called Testing‐Based Forward Model Selection (TBFMS) in linear regression problems. This procedure inductively selects covariates that add predictive power into a working statistical model before estimating a final regression. The criterion for deciding which covariate to include next and when to stop including covariates is derived from a profile of traditional statistical hypothesis tests. This paper proves probabilistic bounds, which depend…

弱识别下三角联立方程模型的非参数估计AI 解读

This paper analyzes the problem of weak instruments on identification, estimation, and inference in a simple nonparametric model of a triangular system. The paper derives a necessary and sufficient rank condition for identification, based on which weak identification is established. Then nonparametric weak instruments are defined as a sequence of reduced‐form functions where the associated rank shrinks to zero. The problem of weak instruments is characterized as concurvity ,…

利用分段线性同伦快速精确构造 lasso 的共形预测集AI 解读

Summary Conformal prediction is a general method that converts almost any point predictor to a prediction set. The resulting set retains the good statistical properties of the original estimator under standard assumptions, and guarantees valid average coverage even when the model is mis-specified. A main challenge in applying conformal prediction in modern applications is efficient computation, as it generally requires an exhaustive search over the entire output space. In…

等方差假设下的因果发现AI 解读

Summary Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variance. We show that this fact is implied by an ordering among conditional variances. We demonstrate that ordering estimates of these variances yields a simple yet state-of-the-art method for causal structure learning that is readily extendable to high-dimensional problems.

高维生物数据中不同可估程度的未观测协变量处理AI 解读

Summary An important phenomenon in high-throughput biological data is the presence of unobserved covariates that can have a significant impact on the measured response. When these covariates are also correlated with the covariate of interest, ignoring or improperly estimating them can lead to inaccurate estimates of and spurious inference on the corresponding coefficients of interest in a multivariate linear model. We first prove that existing methods to account for these…

高维谱统计量的自助法AI 解读

Summary Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of spectral statistics in low-dimensional problems, such methods are relatively unexplored in the high-dimensional setting. The aim of this article is to focus on linear spectral statistics as a class of prototypes for developing a…

通过扰动自助法实现 lasso 的分布一致性AI 解读

Summary The lasso is a popular estimation procedure in multiple linear regression. We develop and establish the validity of a perturbation bootstrap method for approximating the distribution of the lasso estimator in a heteroscedastic linear regression model. We allow the underlying covariates to be either random or nonrandom, and show that the proposed bootstrap method works irrespective of the nature of the covariates. We also investigate finite-sample properties of the…

实证经济学中正则化估计量的选择：机器学习的风险AI 解读

Abstract Many settings in empirical economics involve estimation of a large number of parameters. In such settings, methods that combine regularized estimation and data-driven choices of regularization parameters are useful. We provide guidance to applied researchers on the choice between regularized estimators and data-driven selection of regularization parameters. We characterize the risk and relative performance of regularized estimators as a function of the…

基于趋势滤波的加性模型AI 解读

We study additive models built with trend filtering, that is, additive models whose components are each regularized by the (discrete) total variation of their $k$th (discrete) derivative, for a chosen integer $k\geq0$. This results in $k$th degree piecewise polynomial components, (e.g., $k=0$ gives piecewise constant components, $k=1$ gives piecewise linear, $k=2$ gives piecewise quadratic, etc.). Analogous to its advantages in the univariate case, additive trend filtering…

维度与样本量之比趋零时样本自协方差矩阵的联合收敛及应用AI 解读

Consider a high-dimensional linear time series model where the dimension $p$ and the sample size $n$ grow in such a way that $p/n\to 0$. Let $\hat{\Gamma }_{u}$ be the $u$th order sample autocovariance matrix. We first show that the LSD of any symmetric polynomial in $\{\hat{\Gamma }_{u},\hat{\Gamma }_{u}^{*},u\geq 0\}$ exists under independence and moment assumptions on the driving sequence together with weak assumptions on the coefficient matrices. This LSD result, with…

高维弱假设推断中的自助法与样本分割AI 解读

Several new methods have been recently proposed for performing valid inference after model selection. An older method is sample splitting: use part of the data for model selection and the rest for inference. In this paper, we revisit sample splitting combined with the bootstrap (or the Normal approximation). We show that this leads to a simple, assumption-lean approach to inference and we establish results on the accuracy of the method. In fact, we find new bounds on the…

稀疏 Cholesky 因子高维 DAG 模型的极小极大后验收敛率与选择一致性AI 解读

In this paper we study the high-dimensional sparse directed acyclic graph (DAG) models under the empirical sparse Cholesky prior. Among our results, strong model selection consistency or graph selection consistency is obtained under more general conditions than those in the existing literature. Compared to Cao, Khare and Ghosh [Ann. Statist. (2019) 47 319–348], the required conditions are weakened in terms of the dimensionality, sparsity and lower bound of the nonzero…

高维白噪声检验AI 解读

Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension $p$ is large in relation to the sample size $T$, the popular omnibus tests including the multivariate Hosking and Li–McLeod tests are extremely conservative, leading to substantial power loss. To develop more relevant tests for high-dimensional cases, we…

流形上的涂抹型中心极限定理及其高维球面应用AI 解读

The (CLT) central limit theorems for generalized Fréchet means (data descriptors assuming values in manifolds, such as intrinsic means, geodesics, etc.) on manifolds from the literature are only valid if a certain empirical process of Hessians of the Fréchet function converges suitably, as in the proof of the prototypical BP-CLT [Ann. Statist. 33 (2005) 1225–1259]. This is not valid in many realistic scenarios and we provide for a new very general CLT. In particular, this…

高维协方差矩阵线性结构的假设检验AI 解读

This paper is concerned with test of significance on high dimensional covariance structures, and aims to develop a unified framework for testing commonly-used linear covariance structures. We first construct a consistent estimator for parameters involved in the linear covariance structure, and then develop two tests for the linear covariance structures based on entropy loss and quadratic loss used for covariance matrix estimation. To study the asymptotic properties of the…

高维多响应回归中系数矩阵秩的自适应估计AI 解读

We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the one proposed in Bunea, She and Wegkamp (Ann. Statist. 39 (2011) 1282–1309) in that it does not require estimation of the unknown variance of the noise, nor does it depend on a delicate choice of a tuning parameter. We develop an iterative,…

高维随机化不完全U统计量AI 解读

This paper studies inference for the mean vector of a high-dimensional $U$-statistic. In the era of big data, the dimension $d$ of the $U$-statistic and the sample size $n$ of the observations tend to be both large, and the computation of the $U$-statistic is prohibitively demanding. Data-dependent inferential procedures such as the empirical bootstrap for $U$-statistics is even more computationally expensive. To overcome such a computational bottleneck, incomplete $U$-statis…

排序凹惩罚回归AI 解读

The Lasso is biased. Concave penalized least squares estimation (PLSE) takes advantage of signal strength to reduce this bias, leading to sharper error bounds in prediction, coefficient estimation and variable selection. For prediction and estimation, the bias of the Lasso can be also reduced by taking a smaller penalty level than what selection consistency requires, but such smaller penalty level depends on the sparsity of the true coefficient vector. The sorted $\ell_{1}$ p…

主特征子空间的分布式估计AI 解读

Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication cost can prohibit the computation of PCA in a central location and distributed algorithms for PCA are thus needed. This paper proposes and studies a distributed PCA algorithm: each node machine computes the top $K$ eigenvectors and…