Statistics is the science that focuses on drawing conclusions from data, by modeling and analyzing the data using probabilistic models. In An Introduction to Mathematical Statistics
the authors describe key concepts from statistics and give a mathematical basis for important statistical methods. Much attention is paid to the sound application of those methods to data.
The three main topics in statistics are estimators, tests, and confidence regions. The authors illustrate these in many examples, with a separate chapter on regression models, including linear regression and analysis of variance. They also discuss the optimality of estimators and tests, as well as the selection of the best-fitting model.
Each chapter ends with a case study in which the described statistical methods are applied. This book assumes a basic knowledge of probability theory, calculus, and linear algebra.
Several annexes are available for Mathematical Statistics on this page