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多层矩阵因子模型AI 解读

Large scale matrix data has been widely discovered and continuously studied in various fields recently. We propose a multilevel matrix factor model considering the existence of multi level factor structure in matrix time series. This model incorporates both global factors influencing all matrix time series and local factors confined to impact specific matrix time series. Asymptotic properties are established to ensure the consistency of our procedure for estimating factor…

考虑相关结构的高维两样本均值新检验AI 解读

This paper is concerned with high-dimensional two-sample mean problems, which receive considerable attention in recent literature. To utilize the correlation information among variables for enhancing the power of two-sample mean tests, we consider the setting in which the precision matrix of high-dimensional data possesses a linear structure. Thus, we first propose a new precision matrix estimation procedure with considering its linear structure, and further develop…

高维遗传数据预测中的分块估计与参考面板估计AI 解读

Genetic prediction holds immense promise for translating genetic discoveries into medical advances. As the high-dimensional covariance matrix (or the linkage disequilibrium (LD) pattern) of genetic variants often presents a block-diagonal structure, numerous methods account for the dependence among variants in predetermined local LD blocks. Moreover, due to privacy considerations and data protection concerns, genetic variant dependence in each LD block is typically estimated…

高维模型的双向同时推断AI 解读

This article proposes a general two-directional simultaneous inference (TOSI) framework for high-dimensional models with a manifest variable or latent variable structure, for example, high-dimensional mean models, high-dimensional sparse regression models, and high-dimensional latent factors models. TOSI performs simultaneous inference on a set of parameters from two directions, one to test whether the assumed zero parameters indeed are zeros and one to test whether exist…

超高维混合类型相关变量的广义因子模型AI 解读

As high-dimensional data measured with mixed-type variables gradually become prevalent, it is particularly appealing to represent those mixed-type high-dimensional data using a much smaller set of so-called factors. Due to the limitation of the existing methods for factor analysis that deal with only continuous variables, in this article, we develop a generalized factor model, a corresponding algorithm and theory for ultra-high dimensional mixed types of variables where both…

大样本协方差矩阵尖峰特征值与线性谱统计量的渐近独立性AI 解读

We consider general high-dimensional spiked sample covariance models and show that their leading sample spiked eigenvalues and their linear spectral statistics are asymptotically independent when the sample size and dimension are proportional to each other. As a byproduct, we also establish the central limit theorem of the leading sample spiked eigenvalues by removing the block diagonal assumption on the population covariance matrix, which is commonly needed in the…

通过调整特征值阈值估计因子数量AI 解读

Determining the number of common factors is an important and practical topic in high dimensional factor models. The existing literatures are mainly based on the eigenvalues of the covariance matrix. Due to the incomparability of the eigenvalues of the covariance matrix caused by heterogeneous scales of observed variables, it is very difficult to give an accurate relationship between these eigenvalues and the number of common factors. To overcome this limitation, we appeal to…

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…

高维相关矩阵检验AI 解读

Testing correlation structures has attracted extensive attention in the literature due to both its importance in real applications and several major theoretical challenges. The aim of this paper is to develop a general framework of testing correlation structures for the one-, two-, and multiple sample testing problems under a high-dimensional setting when both the sample size and data dimension go to infinity. Our test statistics are designed to deal with both the dense and…

高维样本协方差矩阵线性谱统计中心极限定理的替换原理及检验应用AI 解读

Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLTs) for linear spectral statistics of high-dimensional noncentralized sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for noncentralized sample covariance matrices, some of which even assume Gaussian-like…

刻画非对称性与非线性的广义相关度量AI 解读

Applicability of Pearson's correlation as a measure of explained variance is by now well understood. One of its limitations is that it does not account for asymmetry in explained variance. Aiming to develop broad applicable correlation measures, we study a pair of generalized measures of correlation (GMC) that deals with asymmetries in explained variances, and linear or nonlinear relations between random variables. We present examples under which the paired measures are…