New book in the Statistics Reading Group: "Asymptotic Stochastics"

The next book to be read in the Statistics Reading Group will be Asymptotic Stochastics by Norbert Henze. The book provides a comprehension-oriented, detailed, and gentle introduction to asymptotic stochastics, covering basic, advanced, and current research topics. It does so by a particular clear and pedagogical style that embraces self-questions, gives historical remarks, and provides numerous examples and solved exercises, thus being a useful resource for lecturers and students.

From the Springer description:

This textbook, which is based on the second edition of a book that has been previously published in German language, provides a comprehension-oriented introduction to asymptotic stochastics. It is aimed at the beginning of a master’s degree course in mathematics and covers the material that can be taught in a four-hour lecture with two-hour exercises. Individual chapters are also suitable for seminars at the end of a bachelor’s degree course.

In addition to more basic topics such as the method of moments in connection with the convergence in distribution or the multivariate central limit theorem and the delta method, the book covers limit theorems for U-statistics, the Wiener process and Donsker’s theorem, as well as the Brownian bridge, with applications to statistics. It concludes with a central limit theorem for triangular arrays of Hilbert space-valued random elements with applications to weighted $L^2$ statistics.

The book is deliberately designed for self-study. It contains 138 self-questions, which are answered at the end of each chapter, as well as 194 exercises with solutions.

As in the previous book, participants are expected to read the content before the sessions. Then, during the session, we will go page by page over the book and discuss its important results, implications, connections, unclear points, etc., documenting in a shared Overleaf document this process, as done previously. Who guides what parts is decided in-session. Sessions are expected to be held weekly.