Xia, Ningning; Bai, Zhidong - In: Statistical Papers 56 (2015) 1, pp. 23-60

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>