This short book elaborates on selected aspects of stochastic-statistical dependencies in multivariate statistics. Each chapter provides a rigorous and self-contained treatment of one specific topic, poses a particular problem within its scope, and concludes by presenting its solution. The presented problems are not only relevant for research in mathematical statistics, but also entertaining, with elegant proofs and appealing solutions. The chapters cover correlation coefficients of bivariate normal distributions, empirical likelihood ratio tests for the population correlation, the rearrangement algorithm, covariances of order statistics, equi-correlation matrices, skew-normal distributions and the weighted bootstrap. This book is primarily intended for early-career researchers in mathematical statistics, but will also be interesting for lecturers in the field. Its goal is to rouse the reader's interest, further their knowledge of the subject and provide them with some useful mathematical techniques.

Autorentext

Thorsten Dickhaus has been a Full Professor of Mathematical Statistics at the University of Bremen, Germany since 2015. He obtained his PhD in mathematics from the Heinrich Heine University, Düsseldorf, Germany in 2008 and held postdoc positions at the German Diabetes Center, Düsseldorf, and the Berlin Institute of Technology. He was a Junior Professor of Mathematical Statistics at the Humboldt University of Berlin. His research interests include multiple testing, asymptotic statistics, the theory of nonparametric tests, resampling and bootstrap techniques, statistical applications in the life sciences, and computational statistics.

Inhalt

Preface.- General preliminaries.- Correlation coefficients of bivariate normal distributions.- Empirical likelihood ratio tests for the population correlation coefficient.- The rearrangement algorithm.- On the covariances of order statistics.- On equi-correlation matrices.- Skew-normal distributions.- The weighted bootstrap.- index.