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高维样本协方差矩阵的广义线性谱统计及其应用AI 解读

In this paper, we introduce the Generalized Linear Spectral Statistics (GLSS) of a high-dimensional sample covariance matrix Sn, denoted as trf(Sn)Bn, which effectively captures distinct spectral properties of Sn by incorporating an ancillary matrix Bn and a test function f. The joint asymptotic normality of GLSS associated with different test functions is established under mild assumptions on Bn and the underlying distribution, when the dimension n and sample size N are…

杨青与童昕对“网络潜在增长过程的根节点与社区推断”的讨论AI 解读

First, we congratulate Dr. Crane and Dr. Xu for this important contribution to statistical network analysis. To address an overlooked fact that most real networks are formed through a growth process, the authors introduce a useful PAPER model and its variations and skilfully construct computationally feasible confidence sets for the root node(s). In the data analysis, the authors also use their models as a new approach to community detection. On this note, our interest lies…

残差子抽样的通用秩推断及其大型网络应用AI 解读

Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. In this paper, we suggest a universal approach to rank inference via residual subsampling (RIRS) for testing and estimating rank in a wide family of models, including many popularly used network models such as the degree corrected mixed membership model as a special case. Our procedure constructs a test statistic via subsampling…

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…

检测高维协方差矩阵微弱与稀疏差异的加权统计量AI 解读

This article considers testing equality of two population covariance matrices when the data dimension p diverges with the sample size n (p/n → c > 0). We propose a weighted test statistic that is data-driven and powerful in both faint alternatives (many small disturbances) and sparse alternatives (several large disturbances). Its asymptotic null distribution is derived by large random matrix theory without assuming the existence of a limiting cumulative distribution function…

竞争风险生存数据的联合推断AI 解读

This article develops joint inferential methods for the cause-specific hazard function and the cumulative incidence function of a specific type of failure to assess the effects of a variable on the time to the type of failure of interest in the presence of competing risks. Joint inference for the two functions are needed in practice because (i) they describe different characteristics of a given type of failure, (ii) they do not uniquely determine each other, and (iii) the…