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利用Lasso进行效应修饰的选择后推断AI 解读

Abstract Effect modification occurs when the effect of the treatment on an outcome varies according to the level of other covariates and often has important implications in decision-making. When there are tens or hundreds of covariates, it becomes necessary to use the observed data to select a simpler model for effect modification and then make valid statistical inference. We propose a two-stage procedure to solve this problem. First, we use Robinson's transformation to…

非可逆并行温度法：可扩展的高度并行 MCMC 方案AI 解读

Abstract Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of N interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of the state space. We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and…

尖峰协方差矩阵主成分的统计推断AI 解读

In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high-dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. In particular, we derive the joint distribution of the extreme eigenvalues and the generalized components of the associated eigenvectors, that is, the projections of the eigenvectors onto arbitrary given direction, assuming that the dimension and sample…

利用辅助信息的大规模多重检验最优错误发现率控制AI 解读

Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are available. Exploiting such auxiliary information can boost statistical power. To this end, we propose a framework based on a two-group mixture model with varying probabilities of being null for different hypotheses a priori, where a…

基于自归一化的高维数据变点推断AI 解读

This article considers change-point testing and estimation for a sequence of high-dimensional data. In the case of testing for a mean shift for high-dimensional independent data, we propose a new test which is based on U-statistic in Chen and Qin (Ann. Statist. 38 (2010) 808–835) and utilizes the self-normalization principle (Shao J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 343–366; Shao and Zhang J. Amer. Statist. Assoc. 105 (2010) 1228–1240). Our test targets dense…

含隐变量的多响应回归自适应估计AI 解读

A prominent concern of scientific investigators is the presence of unobserved hidden variables in association analysis. Ignoring hidden variables often yields biased statistical results and misleading scientific conclusions. Motivated by this practical issue, this paper studies the multivariate response regression with hidden variables, Y=(Ψ∗)TX+(B∗)TZ+E, where Y∈Rm is the response vector, X∈Rp is the observable feature, Z∈RK represents the vector of unobserved hidden…

非稀疏高维线性模型的可检验性AI 解读

Understanding statistical inference under possibly nonsparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity of the corresponding row of the precision matrix of the covariates, not the sparsity of the regression coefficients. We develop new concepts of uniform and essentially uniform nontestability that allow the study of limitations of tests…

高维面板数据截面独立性的最大值—求和检验AI 解读

We consider a testing problem for cross-sectional independence for high-dimensional panel data, where the number of cross-sectional units is potentially much larger than the number of observations. The cross-sectional independence is described through linear regression models. We study three tests named the sum, the max and the max-sum tests, where the latter two are new. The sum test is initially proposed by Breusch and Pagan (1980). We design the max and sum tests for…

高维无岭最小二乘插值中的意外现象AI 解读

Interpolators—estimators that achieve zero training error—have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum ℓ2 norm (“ridgeless”) interpolation least squares regression, focusing on the high-dimensional regime in which the number of unknown parameters p is of the same order as the number of samples n. We consider two different models for the feature…

稀疏高维线性回归：平方误差估计与相变AI 解读

We consider a sparse high-dimensional regression model where the goal is to recover a k-sparse unknown binary vector β∗ from n noisy linear observations of the form Y=Xβ∗+W∈Rn where X∈Rn×p has i.i.d. N(0,1) entries and W∈Rn has i.i.d. N(0,σ2) entries. In the high signal-to-noise ratio regime and sublinear sparsity regime, while the order of the sample size needed to recover the unknown vector information-theoretically is known to be n∗:=2klogp/log(k/σ2+1), no polynomial-time…

贝叶斯模型比较中的自动化先验稳健性分析AI 解读

Summary It is well‐known that the marginal likelihood, the gold standard for Bayesian model comparison, can be sensitive to prior hyperparameter choices. However, most models require computationally intense simulation‐based methods to evaluate the typically high‐dimensional integral of the marginal likelihood expression. Hence, despite the recognition that prior sensitivity analysis is important in this context, it is rarely done in practice. We develop efficient and…

模型复杂度能否提升资产配置表现？机器学习预测模型的证据AI 解读

Summary This study evaluates the benefits of integrating return forecasts from a variety of machine learning and forecast combination methods into an out‐of‐sample asset allocation framework. The economic evaluation of the forecasts shows that model complexity translates to improved results in the majority of cases considered, with shrinkage methods and shallow neural networks generating the highest individual performance. Overall, an investor would consistently realize…

基于高频夏普比率的资产筛选AI 解读

In portfolio choice problems, the classical Mean–Variance model in Markowitz (1952) relies heavily on the covariance structure among assets. As the number and types of assets increase rapidly, traditional methods to estimate the covariance matrix and its inverse suffer from the common issues in high or ultra-high dimensional analysis. To avoid the issue of estimating the covariance matrix with high or ultra-high dimensional data, we propose a fast procedure to reduce…

通过风险因子映射高效估计高维动态协方差：金融风险管理应用AI 解读

This paper aims to explore a modified method of high-dimensional dynamic variance–covariance matrix estimation via risk factor mapping, which can yield a dependence estimation of asset returns within a large portfolio with high computational efficiency. The essence of our methodology is to express the time-varying dependence of high-dimensional return variables using the co-movement concept of returns with respect to risk factors. A novelty of the proposed methodology is to…

稀疏函数型线性判别分析AI 解读

Summary Functional linear discriminant analysis provides a simple yet efficient method for classification, with the possibility of achieving perfect classification. Several methods have been proposed in the literature that mostly address the dimensionality of the problem. On the other hand, there is growing interest in interpretability of the analysis, which favours a simple and sparse solution. In this paper we propose a new approach that incorporates a type of sparsity…

协变量维数发散时的积分条件矩检验及其扩展AI 解读

Summary The classical integrated conditional moment test is a promising method for model checking and its basic idea has been applied to develop several variants. However, in diverging-dimension scenarios, the integrated conditional moment test may break down and has completely different limiting properties from the fixed-dimension case. Furthermore, the related wild bootstrap approximation can also be invalid. To extend this classical test to diverging dimension settings,…

误设广义线性模型中的大规模模型选择AI 解读

Summary Model selection is crucial both to high-dimensional learning and to inference for contemporary big data applications in pinpointing the best set of covariates among a sequence of candidate interpretable models. Most existing work implicitly assumes that the models are correctly specified or have fixed dimensionality, yet both model misspecification and high dimensionality are prevalent in practice. In this paper, we exploit the framework of model selection principles…

广义结构模型中的回代检验AI 解读

Summary We introduce bootstrap tests for semiparametric generalized structured models. These can be used for testing different kinds of model specifications like separability, functional forms and homogeneity of effects, or for performing variable selection in a large class of semiparametric models. The test statistics are based on the comparison of non- and semiparametric alternatives in which both the null hypothesis and the alternative are non- or semiparametric. All…

高维多尺度在线变点检测AI 解读

Abstract We introduce a new method for high-dimensional, online changepoint detection in settings where a p-variate Gaussian data stream may undergo a change in mean. The procedure works by performing likelihood ratio tests against simple alternatives of different scales in each coordinate, and then aggregating test statistics across scales and coordinates. The algorithm is online in the sense that both its storage requirements and worst-case computational complexity per new…

高维分位数回归：卷积平滑与凹正则化AI 解读

Abstract ℓ 1 -penalized quantile regression (QR) is widely used for analysing high-dimensional data with heterogeneity. It is now recognized that the ℓ1-penalty introduces non-negligible estimation bias, while a proper use of concave regularization may lead to estimators with refined convergence rates and oracle properties as the signal strengthens. Although folded concave penalized M-estimation with strongly convex loss functions have been well studied, the extant…

高维线性回归的迁移学习：预测、估计与极小极大最优性AI 解读

Abstract This paper considers estimation and prediction of a high-dimensional linear regression in the setting of transfer learning where, in addition to observations from the target model, auxiliary samples from different but possibly related regression models are available. When the set of informative auxiliary studies is known, an estimator and a predictor are proposed and their optimality is established. The optimal rates of convergence for prediction and estimation are…

促进时间治愈模型的一种扩展AI 解读

We consider the problem of estimating the distribution of time-to-event data that is subject to censoring and for which the event of interest might never occur, that is, some subjects are cured. To model this kind of data in the presence of covariates, one of the leading semiparametric models is the promotion time cure model (Stochastic Models of Tumor Latency and Their Biostatistical Applications (1996) World Scientific), which adapts the Cox model to the presence of cured…

非稀疏高维线性回归的典范阈值估计AI 解读

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix of the data. We propose a new family of estimators, called the canonical thresholding estimators, which pick largest regression coefficients in the canonical form. The estimators admit an explicit form and can be linked to LASSO and…

凸约束高斯序列模型中似然比检验的高维渐近理论AI 解读

In the Gaussian sequence model Y=μ+ξ, we study the likelihood ratio test (LRT) for testing H0:μ=μ0 versus H1:μ∈K, where μ0∈K, and K is a closed convex set in Rn. In particular, we show that under the null hypothesis, normal approximation holds for the log-likelihood ratio statistic for a general pair (μ0,K), in the high-dimensional regime where the estimation error of the associated least squares estimator diverges in an appropriate sense. The normal approximation further…