Testing Independence and Conditional Independence in High Dimensions via Coordinatewise Gaussianization
Prof. Jinyuan CHANG
Guanghua Distinguished Professor
School of Statistics
Southern University of Finance and Economics
Date: 14 October 2025 (Tuesday)
Time: 10:30-12:00
Venue: E22-G015
Host: Prof. Yi DING, Assistant Professor in Business Economics
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.
Speaker
Prof. Jinyuan Chang is Guanghua University Chair Professor at Southwestern University of Finance and Economics; Professor at Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Prof. Chang’s primarily research interest is in large-scale complex data analysis. He has served as Associate Editor for several top international journals in statistics and econometrics, including the Journal of the Royal Statistical Society Series B, Journal of Business & Economic Statistics, and Journal of the American Statistical Association. He has received numerous honors and awards, such as the State Council Special Government Allowance, the First Prize of the Fok Ying Tung Education Foundation Young Faculty Award, the Ministry of Education’s Outstanding Achievement Award in Scientific Research for Higher Education Institutions, and the Sichuan Provincial Youth Science and Technology Award.
All are welcome!
