Mathematical Statistics: A Rigorous Graduate Textbook on Estimation, Hypothesis Testing, and Statistical Decision Theory

Introduction

Mathematical Statistics by A. A. Borokov is a definitive resource for students, researchers, and professionals seeking a rigorous yet accessible treatment of modern statistical theory. Published by CRC Press, this hardcover edition offers a comprehensive exploration of classical and contemporary methods, making it an essential addition to any academic library. Whether you are preparing for advanced studies in statistics or applying statistical techniques in scientific research, this book provides the foundational knowledge and analytical tools needed to excel.

Book Overview

This volume presents a wide-ranging overview of mathematical statistics as it stands today, balancing depth with clarity. Borokov systematically covers the core principles of estimation theory, hypothesis testing, and statistical game theory, while also addressing more complex topics such as multivariate analysis, regression, and pattern recognition. The text is notable for its coherent mathematical rigor and methodological innovations that simplify proofs without sacrificing precision. It brings together classical results and recent advances, many of which are consolidated here for the first time in a single monograph.

Key Highlights

• Comprehensive Coverage: Spans from foundational concepts to advanced topics, including optimal and asymptotically optimal procedures.
• Rigorous Yet Accessible: Maintains mathematical precision while being structured for easy understanding by graduate students and researchers.
• Methodological Improvements: Introduces simplified proofs and novel approaches that streamline complex derivations.
• Unified Presentation: Brings together new results and classical methods in a cohesive framework, avoiding the need to consult multiple sources.

Inside the Book

The book is organized into logical sections that build from basic probability and statistical inference to advanced topics. Early chapters cover the foundations of estimation theory, including unbiasedness, efficiency, and consistency. Subsequent sections delve into hypothesis testing, the Neyman-Pearson lemma, and statistical decision theory. Later chapters address problems involving two or more samples, observations from different distributions, homogeneity testing, regression analysis, variance analysis, and pattern recognition. Throughout, Borokov emphasizes the derivation of optimal procedures and asymptotic properties, providing readers with a deep understanding of both theory and application.

Key Topics

• Foundations of estimation theory and hypothesis testing
• Statistical game theory and decision-making
• Optimal and asymptotically optimal statistical procedures
• Multivariate analysis and regression models
• Variance analysis and homogeneity testing
• Pattern recognition and classification
• Methods for two or more samples and non-identical distributions

Reader Benefits

• Gain a thorough understanding of modern mathematical statistics from a leading authority.
• Learn simplified proofs that make difficult concepts more accessible.
• Access a single-volume reference that consolidates classical and contemporary results.
• Develop the analytical skills needed for research in statistics, data science, and related fields.
• Prepare effectively for advanced coursework and competitive examinations in statistics.

Learning Outcomes

After studying this book, readers will be able to formulate and solve statistical problems using rigorous mathematical methods, derive optimal estimators and tests, understand the foundations of statistical decision theory, and apply advanced techniques such as regression analysis and pattern recognition. The book also equips learners with the ability to critically evaluate statistical procedures and adapt them to real-world data scenarios.

Who Should Read

This book is ideal for graduate students in statistics, mathematics, and related disciplines, as well as researchers and professionals who require a deep understanding of statistical theory. It is also suitable for advanced undergraduate students with a strong background in probability and calculus. Practitioners in data science, econometrics, biostatistics, and engineering will find the theoretical insights invaluable for developing robust analytical solutions.

About the Author

A. A. Borokov is a distinguished mathematician and statistician known for his contributions to probability theory and mathematical statistics. His research has shaped modern statistical methodology, and his textbooks are widely respected for their clarity and rigor. With decades of teaching and research experience, Borokov brings a unique perspective that bridges theory and application.

About the Publisher

CRC Press is a premier publisher of scientific and technical literature, renowned for producing high-quality books in mathematics, statistics, and engineering. Their commitment to academic excellence ensures that every title meets the highest standards of accuracy and scholarship. This hardcover edition is built to last, making it a durable companion for years of study and reference.

Conclusion

Mathematical Statistics by A. A. Borokov is an indispensable guide for anyone serious about mastering the theoretical underpinnings of statistics. Its blend of classical wisdom and modern innovation, coupled with clear exposition and rigorous proofs, makes it a standout choice for students and researchers alike. Order your copy today from Bookshops.in and elevate your understanding of mathematical statistics.