Title: CLT for LSS of large dimensional Kendall rank correlation matrices and its applications
Authors: Runze Li - The Pennsylvania State University (United States)
Qinwen Wang - Fudan University (China)
Zeng Li - Southern University of Science and Technology (China) [presenting]
Abstract: The focus is on the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. The statistical setting covers a wide range of highly skewed and heavy-tailed distributions since we do not require the components to be identically distributed, and do not need any moment conditions. We establish the Central Limit Theorem (CLT)for the linear spectral statistics (LSS) of the Kendalls rank correlation matrices under the Marchenko-Pastur asymptotic regime, in which the dimension diverges to infinity proportionally with the sample size. We further propose three nonparametric procedures for high dimensional independent test and their limiting null distributions are derived by implementing this CLT. The numerical comparisons demonstrate the robustness and superiority of our proposed test statistics under various mixed and heavy-tailed cases.