This paper discusses the relationship between the population spectral distribution and the limit of the empirical spectral distribution in high-dimensional situations. When the support of the limiting spectral distribution is split into several intervals, the population one gains a meaningful...

This paper discusses the problem of testing for high-dimensional covariance matrices. Tests for an identity matrix and for the equality of two covariance matrices are considered when the data dimension and the sample size are both large. Most importantly, the dimension can be much larger than...

In order to investigate property of the eigenvector matrix of sample covariance matrix <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbf {S}_n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi mathvariant="bold">S</mi> <mi>n</mi> </msub> </math> </EquationSource> </InlineEquation>, in this paper, we establish the central limit theorem of linear spectral statistics associated with a new form of empirical spectral distribution <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$H^{\mathbf {S}_n}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>H</mi> <msub> <mi mathvariant="bold">S</mi> <mi>n</mi>...</msub></msup></math></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

In Jin et al. (2014), the limiting spectral distribution (LSD) of a symmetrized auto-cross covariance matrix is derived using matrix manipulation. The goal of this note is to provide a new method to derive the LSD, which greatly simplifies the derivation in Jin et al. (2014). Moreover, as a...