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高维均值的两样本与 ANOVA 检验AI 解读

This paper considers testing the equality of two high dimensional means. Two approaches are utilized to formulate $L_{2}$-type tests for better power performance when the two high dimensional mean vectors differ only in sparsely populated coordinates and the differences are faint. One is to conduct thresholding to remove the nonsignal bearing dimensions for variance reduction of the test statistics. The other is to transform the data via the precision matrix for signal…

高维数据点间距离的渐近正态性及其两样本检验应用AI 解读

Interpoint distances have applications in many areas of probability and statistics. Thanks to their simplicity of computation, interpoint distance-based procedures are particularly appealing for analysing small samples of high-dimensional data. In this paper, we first study the asymptotic distribution of interpoint distances in the high-dimension, low-sample-size setting and show that it is normal under regularity conditions. We then construct a powerful test for the…

依赖条件下恢复高维均值稀疏差异的速率最优方法AI 解读

The paper considers the problem of recovering the sparse different components between two high-dimensional means of column-wise dependent random vectors. We show that dependence can be utilized to lower the identification boundary for signal recovery. Moreover, an optimal convergence rate for the marginal false nondiscovery rate (mFNR) is established under dependence. The convergence rate is faster than the optimal rate without dependence. To recover the sparse signal…

Statistical depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme. In particular, the half-space depth is shown to have many desirable properties and broad applicability. However, the empirical half-space depth is zero outside the convex hull of the data. This property has rendered the empirical…

DD 分类器：基于深度对深度图的非参数分类方法AI 解读

Using the DD-plot (depth vs. depth plot), we introduce a new nonparametric classification algorithm and call it DD-classifier. The algorithm is completely nonparametric, and it requires no prior knowledge of the underlying distributions or the form of the separating curve. Thus, it can be applied to a wide range of classification problems. The algorithm is completely data driven and its classification outcome can be easily visualized in a two-dimensional plot regardless of…

高维协方差矩阵的两样本检验AI 解读

We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance–covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance between two nonoverlapping segments of the high-dimensional random vectors. The tests are applicable (i) when the data dimension is much larger than the sample sizes, namely the “large $p$, small $n$” situations and (ii) without assuming…

多重风险同步监测中极端事件的阈值划分AI 解读

This article develops a threshold system for monitoring airline performance. This threshold system divides the sample space into regions with increasing levels of risk and allows instant assessments of risk level of any observed airline performance. Of particular concern is the performance with extreme risk. In this article, a multivariate extreme value theory approach is used to establish thresholds for signaling varying levels of extremeness in the context of simultaneous…

基于数据深度的多变量间距：非参数多变量容忍区域的构造AI 解读

This paper introduces and studies multivariate spacings. The spacings are developed using the order statistics derived from data depth. Specifically, the spacing between two consecutive order statistics is the region which bridges the two order statistics, in the sense that the region contains all the points whose depth values fall between the depth values of the two consecutive order statistics. These multivariate spacings can be viewed as a data-driven realization of the…