Abstract
Let $\mathbf{A} =\frac{1}{\sqrt{np}}(\mathbf{X} ^{T}\mathbf{X} -p\mathbf{I} _{n})$ where $\mathbf{X} $ is a $p\times n$ matrix, consisting of independent and identically distributed (i.i.d.) real random variables $X_{ij}$ with mean zero and variance one. When $p/n\to\infty$, under fourth moment conditions a central limit theorem (CLT) for linear spectral statistics (LSS) of $\mathbf{A} $ defined by the eigenvalues is established. We also explore its applications in testing whether a population covariance matrix is an identity matrix.
Citation
Binbin Chen. Guangming Pan. "CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size." Bernoulli 21 (2) 1089 - 1133, May 2015. https://doi.org/10.3150/14-BEJ599
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