17: Limiting Spectral Distribution of Large Kendall's Correlation Matrix and its Application

Music City Center 

The limiting spectral distribution (LSD) of high-dimensional Kendall's correlation matrix and tests of independence based on this matrix have been studied in the literature when the observations are absolutely continuous with respect to Lebesgue measure, and are independent and identically distributed. Here the investigation is focused on the LSD of Kendall's correlation matrix under much weaker assumptions which accommodate discrete and/or non-identical distributions, and also identify the limit distribution by using free probability. A graphical test of independence was also proposed under these assumptions.

Limiting Spectral Distribution

, free cumulant, Hoeffding's decomposition

Hoeffding's decomposition, Marcenko Pastur Law

Marcenko Pastur Law

non-crossing partition

random matrix 

Isolated Statisticians