CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size

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.Comment: Published at http://dx.doi.org/10.3150/14-BEJ599 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

How do top- and bottom-performing companies differ in using business analytics?

Purpose Business analytics (BA) has attracted growing attention mainly due to the phenomena of big data. While studies suggest that BA positively affects organizational performance, there is a lack of academic research. The purpose of this paper, therefore, is to examine the extent to which top- and bottom-performing companies differ regarding their use and organizational facilitation of BA. Design/methodology/approach Hypotheses are developed drawing on the information processing view and contingency theory, and tested using multivariate analysis of variance to analyze data collected from 117 UK manufacture companies. Findings Top- and bottom-performing companies differ significantly in their use of BA, data-driven environment, and level of fit between BA and data-drain environment. Practical implications Extensive use of BA and data-driven decisions will lead to superior firm performance. Companies wishing to use BA to improve decision making and performance need to develop relevant analytical strategy to guide BA activities and design its structure and business processes to embed BA activities. Originality/value This study provides useful management insights into the effective use of BA for improving organizational performance