An AUK-based index for measuring and testing the joint dependence of a random vector

Multi-Panel Kendall Plot in Light of an ROC Curve Analysis Applied to Measuring Dependence

The Kendall plot ($\K$-plot) is a plot measuring dependence between the components of a bivariate random variable. The $\K$-plot graphs the Kendall distribution function against the distribution function of $VU$, where $V$ and $U$ are independent uniform $[0,1]$ random variables. We associate $\K$-plots with the receiver operating characteristic ($\ROC$) curve, a well-accepted graphical tool in biostatistics for evaluating the ability of a biomarker to discriminate between two populations. The most commonly used global index of diagnostic accuracy of biomarkers is the area under the $\ROC$ cur…

Measuring and testing dependence by correlation of distances

Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the classical covariance and correlation. Asymptotic properties and applications in testing independence are di…

基于短时间过程数据测量空间关联并检验空间独立性

Measuring spatial association and testing spatial independence based on short time course data

本文基于Bergsma相关系数$ρ$构造适用于短时间过程空间向量的关联统计量，推导其渐近性质，并通过模拟和COVID-19发病率数据应用验证其在空间独立性检验中的有效性。

The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series

This paper proposes the cross-quantilogram to measure the quantile dependence between two time series. We apply it to test the hypothesis that one time series has no directional predictability to another time series. We establish the asymptotic distribution of the cross quantilogram and the corresponding test statistic. The limiting distributions depend on nuisance parameters. To construct consistent confidence intervals we employ the stationary bootstrap procedure; we show the consistency of this bootstrap. Also, we consider the self-normalized approach, which is shown to be asymptotically pi…

高维情形下具有实际显著性的变点——按主动分量度量信号强度

Practically significant change points in high dimension -- measuring signal strength pro active component

本文针对高维时间序列提出检验实际显著变点的复合原假设，构建适应稠密与稀疏信号的枢轴检验，并给出尾界、高维弱不变性原理及模拟与实例验证。

对分类变量的依赖性进行量化与检验

Quantifying and testing dependence to categorical variables

该研究提出分类变量与度量空间通用变量的依赖系数，推导其理论性质与估计量大样本行为，构建服从渐近$\chi^2$分布且一致的独立性检验，可用于经典$K$-样本问题，还拓展了条件依赖系数变体。