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存在协整时的高维预测回归AI 解读

We propose a Least Absolute Shrinkage and Selection Operator (LASSO) estimator of a predictive regression in which stock returns are conditioned on a large set of lagged covariates, some of which are highly persistent and potentially cointegrated. We establish the asymptotic properties of the proposed LASSO estimator and validate our theoretical findings using simulation studies. The application of this proposed LASSO approach to forecasting stock returns suggests that a…

短面板相关性的综合检验AI 解读

Inoue and Solon (2006, Econometric Theory 22, 835–851) presented a test against serial correlation of arbitrary form in fixed-effect models for short panel data. Implementing the test requires choosing a regularization parameter that may severely affect power and for which no optimal selection rule is available. We present a modified version of their test that does not require any regularization parameter. Asymptotic power calculations illustrate the improvement of our…

高维工具变量模型中的不适定估计AI 解读

This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector β0 which is identified through instrumental variables. We allow for eigenvalues of the expected outer product of included and excluded covariates, denoted by M, to shrink to zero as the sample size increases. We propose a novel estimator based on desparsification of an instrumental variable Lasso estimator, which is a regularized version of 2SLS with an additional…

高维因子模型中变点的估计与推断AI 解读

In this paper, we consider the estimation of break points in high-dimensional factor models where the unobserved factors are estimated by principal component analysis (PCA). The factor loading matrix is assumed to have a structural break at an unknown time. We establish the conditions under which the least squares (LS) estimator is consistent for the break date. Our consistency result holds for both large and small breaks. We also find the LS estimator’s asymptotic…

对“高维回归的一种免调参、稳健且高效的方法”的讨论AI 解读

Despite considerable progress over the past two decades, a critical gap remains between the theory and applications of penalized estimation procedures for high-dimensional regression. On the one ha...

高维回归中免手工调参的稳健高效方法AI 解读

We introduce a novel approach for high-dimensional regression with theoretical guarantees. The new procedure overcomes the challenge of tuning parameter selection of Lasso and possesses several appealing properties. It uses an easily simulated tuning parameter that automatically adapts to both the unknown random error distribution and the correlation structure of the design matrix. It is robust with substantial efficiency gain for heavy-tailed random errors while maintaining…

核方法与筛方法结合：稀疏可加模型正则化后的置信带AI 解读

Junwei Lua, Mladen Kolarb & Han Liuc Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA Booth School of Business, The University of Chicago, Chicago, IL Department of Computer Science, Northwestern University, Evanston, IL Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA. CONTACT Junwei Lu junweilu@hsph.harvard.edu Department of Biostatistics, Harvard T. H. Chan School of Public Health,…

桥下的五个巨魔：异步且含噪高频数据的主成分分析AI 解读

We develop a principal component analysis (PCA) for high frequency data. As in Northern fairy tales, there are trolls waiting for the explorer. The first three trolls are market microstructure noise, asynchronous sampling times, and edge effects in estimators. To get around these, a robust estimator of the spot covariance matrix is developed based on the smoothed two-scale realized variance (S-TSRV). The fourth troll is how to pass from estimated time-varying covariance…

非可忽略未响应下的贝叶斯标量对图像回归AI 解读

Medical imaging has become an increasingly important tool in screening, diagnosis, prognosis, and treatment of various diseases given its information visualization and quantitative assessment. The aim of this article is to develop a Bayesian scalar-on-image regression model to integrate high-dimensional imaging data and clinical data to predict cognitive, behavioral, or emotional outcomes, while allowing for nonignorable missing outcomes. Such a nonignorable nonresponse…

面向高维特征预测的定向随机投影AI 解读

Minerva Mukhopadhyaya & David B. Dunsonb Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India Department of Statistical Science, Duke University, Durham, NC Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA. Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA. CONTACT Minerva Mukhopadhyay minervam@iitk.ac.in Department of…

具有共轭满条件分布的自然指数族相关数据贝叶斯层级模型AI 解读

We introduce a Bayesian approach for analyzing (possibly) high-dimensional dependent data that are distributed according to a member from the natural exponential family of distributions. This problem requires extensive methodological advancements, as jointly modeling high-dimensional dependent data leads to the so-called “big n problem.” The computational complexity of the “big n problem” is further exacerbated when allowing for non-Gaussian data models, as is the case here.…

利用辅助信息的自适应稀疏估计AI 解读

The article considers the problem of estimating a high-dimensional sparse parameter in the presence of side information that encodes the sparsity structure. We develop a general framework that involves first using an auxiliary sequence to capture the side information, and then incorporating the auxiliary sequence in inference to reduce the estimation risk. The proposed method, which carries out adaptive Stein’s unbiased risk estimate-thresholding using side information…

带置信保证的交叉验证AI 解读

Cross-validation is one of the most popular model and tuning parameter selection methods in statistics and machine learning. Despite its wide applicability, traditional cross-validation methods tend to overfit, due to the ignorance of the uncertainty in the testing sample. We develop a novel statistically principled inference tool based on cross-validation that takes into account the uncertainty in the testing sample. This method outputs a set of highly competitive candidate…

深度 Knockoff 方法AI 解读

This article introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion measuring the validity of the produced knockoffs is optimized; this criterion is inspired by the popular maximum mean discrepancy in machine learning and can be thought of as measuring the distance to pairwise exchangeability between…

基于逆概率加权的稳健推断AI 解读

Inverse probability weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of “small denominators,” trimming is routinely employed as a regularization strategy. However, ad hoc trimming of the observations renders usual inference procedures invalid for the target estimand, even in large samples. In this article, we first show that the IPW estimator can have different (Gaussian or…

用于子空间收缩的函数型 Horseshoe 先验AI 解读

We introduce a new shrinkage prior on function spaces, called the functional horseshoe prior (fHS), that encourages shrinkage towards parametric classes of functions. Unlike other shrinkage priors for parametric models, the fHS shrinkage acts on the shape of the function rather than inducing sparsity on model parameters. We study the efficacy of the proposed approach by showing an adaptive posterior concentration property on the function. We also demonstrate consistency of…

ℓ₁惩罚稳健估计量的渐近风险与相变AI 解读

Mean square error (MSE) of the estimator can be used to evaluate the performance of a regression model. In this paper, we derive the asymptotic MSE of $l_{1}$-penalized robust estimators in the limit of both sample size $n$ and dimension $p$ going to infinity with fixed ratio $n/p\rightarrow \delta $. We focus on the $l_{1}$-penalized least absolute deviation and $l_{1}$-penalized Huber’s regressions. Our analytic study shows the appearance of a sharp phase transition in the…

高维协方差矩阵的解析非线性收缩AI 解读

This paper establishes the first analytical formula for nonlinear shrinkage estimation of large-dimensional covariance matrices. We achieve this by identifying and mathematically exploiting a deep connection between nonlinear shrinkage and nonparametric estimation of the Hilbert transform of the sample spectral density. Previous nonlinear shrinkage methods were of numerical nature: QuEST requires numerical inversion of a complex equation from random matrix theory whereas…

受控序贯 Monte CarloAI 解读

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in statistics and related fields; for example, for inference in nonlinear non-Gaussian state space models, and in complex static models. Like many Monte Carlo sampling schemes, they rely on proposal distributions which crucially impact their…

贝叶斯结构化线性模型的一般框架AI 解读

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with a large number of frequentist methodologies, there are rather few theoretically optimal Bayes methods for high dimensional models. This paper provides a unified approach to both Bayes high dimensional statistics and Bayes nonparametrics in a general framework of structured linear models. With a proposed two-step prior, we prove a general oracle…

哪种桥估计量最适合变量选择？AI 解读

We study the problem of variable selection for linear models under the high-dimensional asymptotic setting, where the number of observations $n$ grows at the same rate as the number of predictors $p$. We consider two-stage variable selection techniques (TVS) in which the first stage uses bridge estimators to obtain an estimate of the regression coefficients, and the second stage simply thresholds this estimate to select the “important” predictors. The asymptotic false…

基于自归一化的高维时间序列假设检验AI 解读

Self-normalization has attracted considerable attention in the recent literature of time series analysis, but its scope of applicability has been limited to low-/fixed-dimensional parameters for low-dimensional time series. In this article, we propose a new formulation of self-normalization for inference about the mean of high-dimensional stationary processes. Our original test statistic is a U-statistic with a trimming parameter to remove the bias caused by weak dependence.…

社群识别中均值场变分推断的理论与计算保证AI 解读

The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative coordinate ascent variational inference algorithm has been widely applied to large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the mean field method, there exist remarkably little fundamental theoretical justifications. To the best of our knowledge, the iterative algorithm has never been…

因子分析与主成分分析中的置换方法AI 解读

Researchers often have datasets measuring features $x_{ij}$ of samples, such as test scores of students. In factor analysis and PCA, these features are thought to be influenced by unobserved factors, such as skills. Can we determine how many components affect the data? This is an important problem, because decisions made here have a large impact on all downstream data analysis. Consequently, many approaches have been developed. Parallel Analysis is a popular permutation…