Aygul Zagidullina - High-Dimensional Covariance Matrix Estimation: An Introduction to Random Matrix Theory

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SpringerBriefs in Applied Statistics and Econometrics (SBASE) showcase areas of current relevance in the fields of statistical methodology, theoretical and empirical econometrics, statistics in the natural sciences, and financial econometrics. Of interest are topics arising in the analysis of cross-sectional, panel, time-series and high-frequency data. The primary audience of the SBASE series are researchers with an interest in theoretical, empirical and computer-based statistics and econometrics.

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1st edition originally published electronically on KOPS of the University of Konstanz, 2019

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Statistics, as much as any other science, is characterized by a continual and ongoing accumulation of knowledge. As it is difficult to keep up with the subject in its entire breadth, an ever-increasing specialization in the field is unavoidable. Witness the growing body of statistics field journals as well as the rising number of research articles they publish. Because of this development, there is a need for publication outlets that address a broad readership and present challenging material, both new and established, in a self-contained and accessible manner, without requiring specialist background knowledge.

This is the backcloth against which the SpringerBriefs in Applied Statistics and Econometrics (SBASE) were conceived by the German Statistical Society (the Deutsche Statistische Gesellschaft, DStatG) and Springer. The general aim of the SpringerBriefs format, i.e., reports of state-of-the-art techniques, snapshots of emerging topics, or lecture notes making a specialist topic accessible to non-specialist readers, seemed particularly well-suited to address the aforementioned need for manuscripts that are too long for being journal articles and too short as traditional monographs.

We were very grateful for being appointed as the inaugural editors of SBASE. This mandate is both a responsibility and an opportunity to establish this new series as a trusted source of high-quality research. We assembled to that end a superb team of associated editors who, with their expertise and network, provide invaluable support in the refereeing process of manuscripts: H. Peter Boswijk (Universiteit van Amsterdam), Jrg Breitung (Universitt zu Kln), Walter Krmer (Technische Universitt Dortmund), Karl Mosler (Universitt zu Kln), and Peter X. K. Song (University of Michigan). With their help, we are confident that we will edit many exciting projects on statistical and econometric methodology or empirical applications in the natural, social, and economic sciences. We hope that the installments of SBASE will find many interested readers among researchers, practitioners, and policymakers alike.

The present book by Aygul Zagidullina is a worthy first volume of SBASE. Its topic, viz., covariance matrix estimation and random matrix theory, straddles traditional statistics as well as a state-of-the-art technique for dealing with high-dimensional data. The book is thus a timely introduction to a topic that will be of interest to readers in economics, finance, engineering, and the medical sciences. The text will be of particular use to those who have a background in classical statistical inference but seek guidance for dealing with data structures that require a different approach to distribution theory. Aygul Zagidullina provides a lucid and insightful bridge between these challenging strands of the literature.