Rounding errors have a considerable impact on statistical inferences, especially when the data size is large and the finite normal mixture model is very important in many applied statistical problems, such as bioinformatics. In this article, we investigate the statistical impacts of rounding...

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>