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区间响应的特征筛选：招聘工资与技能要求的关联AI 解读

It is important to quantify the differences in returns to skills using the online job advertisements data, which have attracted great interest in both labor economics and statistics fields. In this paper, we study the relationship between the posted salary and the job requirements in online labor markets. There are two challenges to deal with. First, the posted salary is always presented in an interval-valued form, for example, 5k-10k yuan per month. Simply taking the…

变系数中介模型及其在行为经济学数据分析中的应用AI 解读

This paper is concerned with causal mediation analysis with varying indirect and direct effects. We propose a varying coefficient mediation model, which can also be viewed as an extension of moderation analysis on a causal diagram. We develop a new estimation procedure for the direct and indirect effects based on B-splines. Under mild conditions, rates of convergence and asymptotic distributions of the resulting estimates are established. We further propose a F-type test for…

协方差—均值回归的统计推断AI 解读

In this article, we introduce a covariance-mean regression model with heterogeneous similarity matrices. It not only links the covariance of responses to heterogeneous similarity matrices induced by auxiliary information, but also establishes the relationship between the mean of responses and covariates. Under this new model setting, however, two statistical inference challenges are encountered. The first challenge is that the consistency of the covariance estimator based on…

高维中介分析：筛选连接童年创伤与皮质醇应激反应的 DNA 甲基化位点AI 解读

Childhood trauma tends to influence cortisol stress reactivity through the mediating effects of DNA methylation. Houtepen et al. conducted a study to investigate the role of DNA methylation in cortisol stress reactivity and its relationship with childhood trauma. The study collected a dataset consisting of 385,882 DNA methylation loci, cortisol stress reactivity, one-dimensional score on a childhood trauma questionnaire and several covariates for 85 healthy individuals. Of…

超高维监督学习特征筛选中的协变量信息数AI 解读

Contemporary high-throughput experimental and surveying techniques give rise to ultrahigh-dimensional supervised problems with sparse signals; that is, a limited number of observations (n), each with a very large number of covariates (p≫n), only a small share of which is truly associated with the response. In these settings, major concerns on computational burden, algorithmic stability, and statistical accuracy call for substantially reducing the feature space by eliminating…

基于模式导向抽样的大规模数据流监测AI 解读

Monitoring large-scale datastreams with limited resources has become increasingly important for real-time detection of abnormal activities in many applications. Despite the availability of large datasets, the challenges associated with designing an efficient change-detection when clustering or spatial pattern exists are not yet well addressed. In this article, a design-adaptive testing procedure is developed when only a limited number of streaming observations can be…

利用 Knockoff 特征进行无模型特征筛选与错误发现率控制AI 解读

This article proposes a model-free and data-adaptive feature screening method for ultrahigh-dimensional data. The proposed method is based on the projection correlation which measures the dependence between two random vectors. This projection correlation based method does not require specifying a regression model, and applies to data in the presence of heavy tails and multivariate responses. It enjoys both sure screening and rank consistency properties under weak…

通过递归在线得分估计进行高维模型推断AI 解读

In this paper, we develop a new estimation and valid inference method for single or low-dimensional regression coefficients in high-dimensional generalized linear models. The number of the predictors is allowed to grow exponentially fast with respect to the sample size. The proposed estimator is computed by solving a score function. We recursively conduct model selection to reduce the dimensionality from high to a moderate scale and construct the score equation based on the…

高维 Kendall 秩相关矩阵线性谱统计量的中心极限定理及应用AI 解读

This paper is concerned with the limiting spectral behaviors of large dimensional Kendall’s rank correlation matrices generated by samples with independent and continuous components. The statistical setting in this paper covers a wide range of highly skewed and heavy-tailed distributions since we do not require the components to be identically distributed, and do not need any moment conditions. We establish the central limit theorem (CLT) for the linear spectral statistics…

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…

高维纵向数据的显著性检验AI 解读

This paper concerns statistical inference for longitudinal data with ultrahigh dimensional covariates. We first study the problem of constructing confidence intervals and hypothesis tests for a low dimensional parameter of interest. The major challenge is how to construct a powerful test statistic in the presence of high-dimensional nuisance parameters and sophisticated within-subject correlation of longitudinal data. To deal with the challenge, we propose a new quadratic…

高维均值向量的经验似然检验AI 解读

Summary This paper is concerned with empirical likelihood inference on the population mean when the dimension $p$ and the sample size $n$ satisfy $p/n\rightarrow c\in [1,\infty)$. As shown in Tsao (2004), the empirical likelihood method fails with high probability when $p/n>1/2$ because the convex hull of the $n$ observations in $\mathbb{R}^p$ becomes too small to cover the true mean value. Moreover, when $p> n$, the sample covariance matrix becomes singular, and this…

基于重拟合交叉验证的超高维精度矩阵估计AI 解读

This paper develops a new estimation procedure for ultrahigh dimensional sparse precision matrix, the inverse of covariance matrix. Regularization methods have been proposed for sparse precision matrix estimation, but they may not perform well with ultrahigh dimensional data due to the spurious correlation. We propose a refitted cross validation (RCV) method for sparse precision matrix estimation based on its Cholesky decomposition, which does not require the Gaussian…

通过样本分割一致选择变点数量AI 解读

In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and…

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…

高维广义线性模型的线性假设检验AI 解读

This paper is concerned with testing linear hypotheses in high dimensional generalized linear models. To deal with linear hypotheses, we first propose the constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test…

高维纵向数据协方差矩阵的同质性检验AI 解读

Summary This paper deals with the detection and identification of changepoints among covariances of high-dimensional longitudinal data, where the number of features is greater than both the sample size and the number of repeated measurements. The proposed methods are applicable under general temporal-spatial dependence. A new test statistic is introduced for changepoint detection, and its asymptotic distribution is established. If a changepoint is detected, an estimate of…

大规模社交网络中的门户节点筛选AI 解读

Network autoregression model (NAM), as a powerful tool to study user social behaviors on large scale social networks, has drawn great attention in recent years. In this paper, we are interested in identifying the influential users (i.e., portal nodes) in a social network under the framework of NAM. Especially, we consider the autoregression model that allows to have a heterogeneous and sparse network effect coefficients. Therefore, the portal nodes take influential powers…

超高维加性模型中的误差方差估计AI 解读

Error variance estimation plays an important role in statistical inference for high-dimensional regression models. This article concerns with error variance estimation in high-dimensional sparse additive model. We study the asymptotic behavior of the traditional mean squared errors, the naive estimate of error variance, and show that it may significantly underestimate the error variance due to spurious correlations that are even higher in nonparametric models than linear…

两个随机向量之间的投影相关AI 解读

We propose the use of projection correlation to characterize dependence between two random vectors. Projection correlation has several appealing properties. It equals zero if and only if the two random vectors are independent, it is not sensitive to the dimensions of the two random vectors, it is invariant with respect to the group of orthogonal transformations, and its estimation is free of tuning parameters and does not require moment conditions on the random vectors. We…

基于分位数偏相关的变量筛选AI 解读

In quantile linear regression with ultra-high dimensional data, we propose an algorithm for screening all candidate variables and subsequently selecting relevant predictors. Specifically, we first employ quantile partial correlation for screening, and then we apply the extended Bayesian information criterion (EBIC) for best subset selection. Our proposed method can successfully select predictors when the variables are highly correlated, and it can also identify variables…

高维线性模型中单个回归系数的检验AI 解读

In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the…

Harris 常返马尔可夫过程的局部复合分位数回归平滑AI 解读

In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity restriction on the model, and allow that the regressors are generated by a general…

This paper is concerned with the problem of feature screening for multi-class linear discriminant analysis under ultrahigh dimensional setting. We allow the number of classes to be relatively large. As a result, the total number of relevant features is larger than usual. This makes the related classification problem much more challenging than the conventional one, where the number of classes is small (very often two). To solve the problem, we propose a novel pairwise sure…