论文检索

高维主成分分析中显著成分数量的估计AI 解读

Abstract We consider the problem of estimating the number of significant components in high-dimensional principal component analysis. We propose a new penalized approach using the explained variance ratio and the rigidity of the nonspiked sample eigenvalues of sample covariance matrices of $ p $ variables. Compared with methods in the existing literature, the consistency of the proposed estimator holds, not only for independent data, but also for some times series data when…

通过特征值分析识别高维时间序列结构AI 解读

Cross-sectional structures and temporal tendency are important features of high-dimensional time series. Based on eigen-analysis on sample covariance matrices, we propose a novel approach to identifying four popular structures of high-dimensional time series, which are grouped in terms of factor structures and stationarity. The proposed three-step method includes a ratio statistic of empirical eigenvalues;a projected Augmented Dickey-Fuller Test;a new unit-root test based on…

用于高维时间序列聚类的因子建模AI 解读

We propose a new unsupervised learning method for clustering a large number of time series based on a latent factor structure.Each cluster is characterized by its own cluster-specific factors in addition to some common factors which impact on all the time series concerned.Our setting also offers the flexibility that some time series may not belong to any clusters.The consistency with explicit convergence rates is established for the estimation of the common factors, the…

超高维协方差矩阵序列中的变化点估计AI 解读

This article considers the problem of estimating a change point in the covariance matrix in a sequence of high-dimensional vectors, where the dimension is substantially larger than the sample size. A two-stage approach is proposed to efficiently estimate the location of the change point. The first step consists of a reduction of the dimension to identify elements of the covariance matrices corresponding to significant changes. In a second step, we use the components after…

高维非平稳时间序列最大特征值的中心极限定理与单位根检验AI 解读

Let $\{Z_{ij}\}$ be independent and identically distributed (i.i.d.) random variables with $EZ_{ij}=0$, $E\vert Z_{ij}\vert^{2}=1$ and $E\vert Z_{ij}\vert^{4}<\infty$. Define linear processes $Y_{tj}=\sum_{k=0}^{\infty}b_{k}Z_{t-k,j}$ with $\sum_{i=0}^{\infty}\vert b_{i}\vert <\infty$. Consider a $p$-dimensional time series model of the form $\mathbf{x}_{t}=\boldsymbol{\Pi} \mathbf{x}_{t-1}+\Sigma^{1/2}\mathbf{y}_{t},\ 1\leq t\leq T$ with $\mathbf{y}_{t}=(Y_{t1},\ldots,Y_{tp})'$…

高维相关矩阵：中心极限定理及其应用AI 解读

Summary Statistical inferences for sample correlation matrices are important in high dimensional data analysis. Motivated by this, the paper establishes a new central limit theorem for a linear spectral statistic of high dimensional sample correlation matrices for the case where the dimension p and the sample size n are comparable. This result is of independent interest in large dimensional random-matrix theory. We also further investigate the sample correlation matrices of…

大量高维随机向量之间的独立性检验AI 解读

Capturing dependence among a large number of high-dimensional random vectors is a very important and challenging problem. By arranging n random vectors of length p in the form of a matrix, we develop a linear spectral statistic of the constructed matrix to test whether the n random vectors are independent or not. Specifically, the proposed statistic can also be applied to n random vectors, each of whose elements can be written as either a linear stationary process or a…