Tracy-Widom law for the extreme eigenvalues of sample correlation matrices

• Main Authors: Bao, Zhigang, Pan, Guangming, Zhou, Wang
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Online Access: https://hdl.handle.net/10356/96096; http://hdl.handle.net/10220/10085
• Institution: Nanyang Technological University

Let the sample correlation matrix be W = YYT, where Y = (yij)p,n with yij = xij /√∑xij2. We assume {xij : 1 ≤ i ≤ p, 1 ≤ j ≤ n} to be a collection of independent symmetrically distributed random variables with sub-exponential tails. Moreover, for any i, we assume xij, 1 ≤ j ≤ n to be identically dis...