CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size - Chen, Binbin (2015)
Let A = 1/√np(XT X−pIn) where X is a p×n matrix, consisting of independent and identically distributed (i.i.d.) real random variables Xij with mean zero and variance one. When p/n→∞, under fourth moment conditions a central limit theorem (CLT) for linear spectral statistics (LSS) of A defined by the eigenvalues is established. We also explore its applications in testing whether a population covariance matrix is an identity matrix.