The paper titled “Testing Independence and Conditional Independence in High Dimensions via Coordinatewise Gaussianization,” co-authored by Prof. Jingyuan Chang, doctoral candidate Yue Du, Prof. Jing He of Xiamen University, and Prof. Qiwei Yao of the London School of Economics and Political Science, has been officially accepted by the Journal of the American Statistical Association, one of the leading international journals in the field of statistics.
Abstract
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each component variable to the standard normal via its marginal empirical distribution, and we then test for independence and conditional independence of the transformed random vectors using appropriate L∞-type test statistics. While we are testing some necessary conditions of the independence or the conditional independence, the new tests outperform the 13
frequently used testing methods in a large scale simulation comparison. The advantage of the new tests can be summarized as follows: (i) they do not require any moment conditions, (ii) they allow arbitrary dependence structures of the components among the random vectors, and (iii) they allow the dimensions of random vectors to diverge at the exponential rates of the sample size. The critical values of the proposed tests are determined by a computationally efficient multiplier bootstrap procedure. Theoretical analysis shows that the sizes of the proposed tests can be well controlled by the nominal significance level, and the proposed tests are also consistent under certain local alternatives. The finite sample performance of the new tests is illustrated via extensive simulation studies and a real data application.
Author Introduction
Jinyuan Chang is the Executive Director of the Joint Laboratory of Data Science and Business Intelligence at Southwestern University of Finance and Economics. He is a Guanghua Chair Professor and a recipient of the National Science Fund for Distinguished Young Scholars of China. He primarily engaged in research related to complex data analysis.
Yue Du is a doctoral student at the Joint Laboratory of Data Science and Business Intelligence, Southwestern University of Finance and Economics. Her main research interests include hypothesis testing for ultra-high-dimensional data and matrix time series analysis.
Jing He is an Associate Professor and Master’s Supervisor at the School of Statistics, Southwestern University of Finance and Economics. She primarily engaged in research in fields such as high-dimensional data analysis and spatio-temporal data analysis.
Qiwei Yao is a Chair Professor at the London School of Economics. His research interests include time series analysis, dimensionality reduction, factor modeling, dynamic network modeling, spatiotemporal modeling, financial econometrics, and nonparametric regression.
