Mathematical Statistics is a graduate level textbook providing the reader with an adequate base and a reference for further study. There are many books on this topic; not many, however, can be proud of their usefulness to students. This text falls into the good book category, i.e., it is a book that will be of great use to students in their understanding and learning of the concepts. This is primarily due to its style of writing, explaining theories in a narrative way with concrete examples and illustrations.
Out of eight chapters, only chapter one was not so impressive; it seems very rushed and thrown in. However, this is also an introductory chapter and in the rest of the book this style is no longer used, but rather the author offers intuitive reasoning along with plenty of examples and detailed presentation of proofs. The last chapter again serves the purpose of an introduction, this time to linear algebra.
This book is for mathematically-inclined readers. It is full of theorems. As already noted, the proofs that are presented are detailed and very seldom can one find hand-waving. This indeed is an approach to be welcomed. The book has many examples, which don't just serve the purpose of existence but are diced down to details. Each chapter contains numerous exercises, which should further improve the understanding if completed. Naturally the majority of the exercises are of a theoretical nature. To make life even better, the book is accompanied with a solutions manual (apparently available only as part of a set with this volume) containing all the exercises and their solutions.
This book should come in handy to all graduate students in statistics both as a study guide and later as a reference.
Ita Cirovic Donev holds a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical methods for credit and market risk. Apart from the academic work she does statistical consulting work for financial institutions in the area of risk management.