This paper discusses the problem of estimating the population spectral distribution from high-dimensional data. We present a general estimation procedure that covers situations where the moments of this distribution fail to identify the model parameters. The main idea is to use generalized...

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>