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病例—对照设计下高维 Logistic 回归的选择后推断AI 解读

Confidence sets are of key importance in high-dimensional statistical inference. Under case–control study, a popular response-selective sampling design in medical study or econometrics, we consider the confidence intervals and statistical tests for single or low-dimensional parameters in high-dimensional logistic regression model. The asymptotic properties of the resulting estimators are established under mild conditions. We also study statistical tests for testing more…

含随机效应的自回归面板有序 Probit 模型的复合似然估计AI 解读

Modeling and estimating autocorrelated discrete data can be challenging. In this article, we use an autoregressive panel ordered probit model where the serial correlation in the discrete variable is driven by the autocorrelation in the latent variable. In such a nonlinear model, the presence of a lagged latent variable results in an intractable likelihood containing high-dimensional integrals. To tackle this problem, we use composite likelihoods that involve a much lower…

通过 Classifier-Lasso 检测有效价格中的未观测异质性AI 解读

This article proposes a new measure of efficient price as a weighted average of bid and ask prices, where the weights are constructed from the bid-ask long-run relationships in a panel error-correction model (ECM). To allow for heterogeneity in the long-run relationships, we consider a panel ECM with latent group structures so that all the stocks within a group share the same long-run relationship and do not otherwise. We extend the Classifier-Lasso method to the ECM to…

股票市场的统计循环随机波动率模型AI 解读

The stochastic volatility (SV) model and its variants are widely used in the financial sector, while recurrent neural network (RNN) models are successfully used in many large-scale industrial applications of deep learning. We combine these two methods in a nontrivial way and propose a model, which we call the statistical recurrent stochastic volatility (SR-SV) model, to capture the dynamics of stochastic volatility. The proposed model is able to capture complex volatility…

高维删失回归模型的 ℓ1 惩罚成对差分估计AI 解读

High-dimensional data are nowadays readily available and increasingly common in various fields of empirical economics. This article considers estimation and model selection for a high-dimensional censored linear regression model. We combine l1-penalization method with the ideas of pairwise difference and propose an l1-penalized pairwise difference least absolute deviations (LAD) estimator. Estimation consistency and model selection consistency of the estimator are…

高维向量自回归模型的速率最优稳健估计AI 解读

High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series, but also the existence of aberrant observations, such as missing values, contaminated observations, and heavy-tailed distributions. For high-dimensional vector autoregressive (VAR) models, we introduce a unified estimation procedure that is…

最优应对 RKHS 非参数回归中的协变量偏移AI 解读

We study the covariate shift problem in the context of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We focus on two natural families of covariate shift problems defined using the likelihood ratios between the source and target distributions. When the likelihood ratios are uniformly bounded, we prove that the kernel ridge regression (KRR) estimator with a carefully chosen regularization parameter is minimax rate-optimal (up to a log factor) for a…

近似流形上的深度非参数回归：具有多项式前因子的非渐近误差界AI 解读

We study the properties of nonparametric least squares regression using deep neural networks. We derive nonasymptotic upper bounds for the excess risk of the empirical risk minimizer of feedforward deep neural regression. Our error bounds achieve minimax optimal rate and improve over the existing ones in the sense that they depend polynomially on the dimension of the predictor, instead of exponentially on dimension. We show that the neural regression estimator can circumvent…

Z₂ 同步中 TAP 自由能的局部凸性与 AMP 收敛AI 解读

We study mean-field variational Bayesian inference using the TAP approach, for Z2-synchronization as a prototypical example of a high-dimensional Bayesian model. We show that for any signal strength λ>1 (the weak-recovery threshold), there exists a unique local minimizer of the TAP free energy functional near the mean of the Bayes posterior law. Furthermore, the TAP free energy in a local neighborhood of this minimizer is strongly convex. Consequently, a…

凸正则化估计量的去偏与线性模型区间估计AI 解读

New upper bounds are developed for the L2 distance between ξ/Var[ξ]1/2 and linear and quadratic functions of z∼N(0,In) for random variables of the form ξ=z⊤f(z)−divf(z). The linear approximation yields a central limit theorem when the squared norm of f(z) dominates the squared Frobenius norm of ∇f(z) in expectation. Applications of this normal approximation are given for the asymptotic normality of debiased estimators in linear regression with correlated design and convex…

利用离散傅里叶变换检验高维因子模型的结构变化AI 解读

We propose a new test for structural changes in large dimensional factor models using a discrete Fourier transform (DFT) approach. When structural changes occur, the conventional principal component analysis may fail to estimate the common factors and factor loadings consistently, and the estimated residuals contain information about the structural changes. This allows us to compare the DFT of the estimated residuals weighted by the estimated common factors with the null…

含缺失观测的高维潜在因子模型及其因果推断应用AI 解读

This paper develops the inferential theory for latent factor models estimated from large dimensional panel data with missing observations. We propose an easy-to-use all-purpose estimator for a latent factor model by applying principal component analysis to an adjusted covariance matrix estimated from partially observed panel data. We derive the asymptotic distribution for the estimated factors, loadings and the imputed values under an approximate factor model and general…

潜在因子模型的信息准则：因子广泛性与自适应性AI 解读

We study the information criteria extensively under general conditions for high-dimensional latent factor models. Upon carefully analyzing the estimation errors of the principal component analysis method, we establish theoretical results on the estimation accuracy of the latent factor scores, incorporating the impact from possibly weak factor pervasiveness; our analysis does not require the same factor strength of all the leading factors. To estimate the number of the latent…

高维因子模型突变点的拟极大似然估计AI 解读

This paper proposes a quasi-maximum likelihood (QML) estimator of the break point for large-dimensional factor models with a single structural break in the factor loading matrix. We show that the QML estimator is consistent for the true break point when the covariance matrix of the pre- or post-break factor loading (or both) is singular. Consistency here means that the deviation of the estimated break date from the true break date k0 converges to zero as the sample size…

含共同因子的高维向量自回归模型AI 解读

This paper studies high-dimensional vector autoregressions (VARs) augmented with common factors that allow for strong cross-sectional dependence. Models of this type provide a convenient mechanism for accommodating the interconnectedness and temporal co-variability that are often present in large dimensional systems. We propose an ℓ1-nuclear-norm regularized estimator and derive the non-asymptotic upper bounds for the estimation errors as well as large sample asymptotics for…

大型因子模型多重结构突变的组融合 LASSO 方法AI 解读

This paper reformulates the identification of multiple structural breaks in factor loadings as a problem of detecting structural breaks in a factor regression, where the estimated pseudo factor corresponding to the largest eigenvalue is regressed on the remaining estimated factors. As a result, a group fused Lasso based estimation procedure is proposed to identify the break dates. Our procedure is practically easy-to-implement with standard statistical packages, overcoming…

因子结构误差下网络溢出效应的收缩估计AI 解读

This paper explores the estimation of a panel data model with cross-sectional interaction that is flexible both in its approach to specifying the network of connections between cross-sectional units, and in controlling for unobserved heterogeneity. It is assumed that there are different sources of information available on a network, which can be represented in the form of multiple weights matrices. These matrices may reflect observed links, different measures of…

高维回归中的推断AI 解读

Abstract This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter, the remaining coefficients being nuisance parameters, and seeks an optimal interest-respecting transformation, inducing sparsity on the relevant blocks of the notional Fisher information matrix. The induced sparsity is exploited…

用于神经网络贝叶斯学习与 MCMC 的迹类高斯先验AI 解读

Abstract This paper introduces a new neural network based prior for real valued functions. Each weight and bias of the neural network has an independent Gaussian prior, with the key novelty that the variances decrease in the width of the network in such a way that the resulting function is well defined in the limit of an infinite width network. We show that the induced posterior over functions is amenable to Monte Carlo sampling using Hilbert space Markov chain Monte Carlo…

种子二元分割：快速且最优的变点检测通用方法AI 解读

Summary We propose seeded binary segmentation for large-scale changepoint detection problems. We construct a deterministic set of background intervals, called seeded intervals, in which single changepoint candidates are searched for. The final selection of changepoints based on these candidates can be done in various ways, adapted to the problem at hand. The method is thus easy to adapt to many changepoint problems, ranging from univariate to high dimensional. Compared to…

倾向得分在观察性因果研究设计中的作用AI 解读

Summary The design of any study, whether experimental or observational, that is intended to estimate the causal effects of a treatment condition relative to a control condition refers to those activities that precede any examination of outcome variables. As defined in our 1983 article (Rosenbaum & Rubin, 1983), the propensity score is the unit-level conditional probability of assignment to treatment versus control given the observed covariates; so the propensity score…

高维响应多元回归的响应变量最优子集选择AI 解读

Summary This article investigates the statistical problem of response-variable selection with high-dimensional response variables and a diverging number of predictor variables with respect to the sample size in the framework of multivariate linear regression. A response best-subset selection model is proposed by introducing a 0-1 selection indicator for each response variable, and then a response best-subset selector is developed by introducing a separation parameter and a…

具有有限样本保证的简明通用去偏机器学习定理AI 解读

Summary Debiased machine learning is a meta-algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e., scalar summaries, of machine learning algorithms. For example, an analyst may seek the confidence interval for a treatment effect estimated with a neural network. We present a non-asymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies…

高维高斯图模型的统一推断AI 解读

Summary Graphical models have become a popular tool for representing dependencies within large sets of variables and are crucial for representing causal structures. We provide results for uniform inference on high-dimensional graphical models, in which the number of target parameters $d$ is potentially much larger than the sample size, under approximate sparsity. Our results highlight how graphical models can be estimated and recovered using modern machine learning methods…