Lectures on Mathematical Statistics - Yisong Yang

This book presents a concise yet comprehensive introduction to the core theory of mathematical statistics. By integrating fundamental probability theory with modern inferential methods, it offers a logically coherent progression from the basic principles of estimation and testing to Bayesian inference and regression.

Although compact, the book is thorough in its treatment of the essential architecture of statistical inference. Key topics include sampling theory, point and interval estimation, parametric and nonparametric inference, hypothesis testing, Bayesian methods, correlation, regression, and logistic modeling. Each Lecture provides carefully chosen examples, full proofs or validations of major results, and exercises designed to consolidate understanding.

The text comprises fifteen focused Lectures, each designed to correspond to one or two class sessions. This structure allows the material to be covered comfortably in a single semester while providing a rigorous foundation for upper-undergraduate and graduate students, as well as practitioners. The exposition emphasizes transparent derivations and conceptual motivation rather than formulaic presentation, reflecting the author’s aim to make every result both intuitively and mathematically meaningful.