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通过度量空间中的度量分布函数开展非参数统计推断AI 解读

The distribution function is essential in statistical inference and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates a paradigm for statistical inference. However, existing distribution functions are defined in Euclidean spaces and are no longer convenient to use in rapidly evolving data objects of complex nature. It is imperative to develop the…

球协方差：Banach 空间中的通用依赖度量AI 解读

Technological advances in science and engineering have led to the routine collection of large and complex data objects, where the dependence structure among those objects is often of great interest. Those complex objects (e.g, different brain subcortical structures) often reside in some Banach spaces, and hence their relationship cannot be well characterized by most of the existing measures of dependence such as correlation coefficients developed in Hilbert spaces. To…

一种通用的确定独立筛选程序AI 解读

Wenliang Pana, Xueqin Wanga, Weinan Xiaoa & Hongtu Zhub*a Department of Statistical Science, School of Mathematics, Sun Yat-Sen University, Guangzhou, P. R. Chinab Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TXCONTACT Hongtu Zhu hzhu5@mdanderson.org Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030Supplementary materials for this article are available online. Please go to…

球散度：非参数两样本检验AI 解读

In this paper, we first introduce Ball Divergence, a novel measure of the difference between two probability measures in separable Banach spaces, and show that the Ball Divergence of two probability measures is zero if and only if these two probability measures are identical without any moment assumption. Using Ball Divergence, we present a metric rank test procedure to detect the equality of distribution measures underlying independent samples. It is therefore robust to…

Statistical inference on conditional dependence is essential in many fields including genetic association studies and graphical models. The classic measures focus on linear conditional correlations, and are incapable of characterizing non-linear conditional relationship including non-monotonic relationship. To overcome this limitation, we introduces a nonparametric measure of conditional dependence for multivariate random variables with arbitrary dimensions. Our measure…