Lectures on Mathematical Statistics

Erscheinungsjahr 2027
ISBN: 978-3-032-27377-2
Verlag: Springer Nature Switzerland AG

Buch, Englisch, 392 Seiten, Format (B × H): 155 mm x 235 mm

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Yang, Yisong

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Bayesianische Inferenz
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen

Inhaltsverzeichnis

Chapter 1 Basic Facts, Concepts, and Ideas.- Chapter 2 Sampling Theory.- Chapter 3 Confidence Intervals.- Chapter 4 Confidence Intervals for Variance.- Chapter 5 Nonparametric Inference.- Chapter 6 Hoeffding’s Inequality and Related Topics.- Chapter 7 Methods of Parametric Inference.- Chapter 8 Asymptotic Normality and Fisher Information.- Chapter 9 Hypothesis Testing—Concepts, Formalism, and Methods.- Chapter 10 Hypothesis Testing Involving Two Populations.- Chapter 11 Bayes’ Method of Estimation.- Chapter 12 Regression and Correlation.- Chapter 13 Bivariate Normal Regression and Correlation Analysis.- Chapter 14 Logistic Regression and Applications.- Chapter 15 Brief Overview of Some Further Topics of Interest.

Über Autor(innen)

Yisong Yang is a Professor of Mathematics at New York University. He has published monographs and textbooks with Springer-Verlag, Cambridge University Press, and Oxford University Press. His research spans mathematical physics, partial differential equations, and applied mathematics. He has taught mathematical statistics and probability for many years, emphasizing clarity, rigor, and conceptual unity in his approach to statistical education.