Mathematical statistics

Guoliang Tian, Xuejun Jiang

Parution le 03/02/2026

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Résumé

Mathematical Statistics is a comprehensive undergraduate textbook developed from the authors' 18 years of teaching experience at The University of Hong Kong (HKU) and Southern University of Science and Technology (SUSTech). Tailored for undergraduates in Statistics, Data Science and Big Data Technology, as well as graduate students in engineering-related fields, it covers core topics of mathematical statistics with logical rigor-from foundational probability theory to point estimation, interval estimation, hypothesis testing, and key concepts like sufficient statistics and Fisher information. What sets it apart is the inclusion of unique content rarely found in standard textbooks: Inverse Bayes Formulae, the Definition of Valid Categorical Distribution, and a Unified Expectation Technique, bridging theoretical depth with practical relevance for real-world data science applications.Distinctive features of this book include:1. Innovative Warp-Weft Dual Structure: In addition to the traditional chapter-section "Warp" framework, the book introduces a self-contained "Weft" thread, resulting in a concise and lucid overall structure. This design enables readers to quickly grasp core concepts, key knowledge points, and challenging topics even before completing the book, thereby streamlining the organization of information.2. Motivation-Driven Conceptualization: When introducing fundamental concepts (e.g., score functions, Cramér-Rao inequality, confidence intervals), the book emphasizes the underlying motivation-the rationale and practical value behind each concept-to promote genuine understanding other than rote memorization.3. Dual Function as Textbook and Presentation: Combining the rigor of a traditional textbook with the clarity of classroom slides, the electronic PDF version can be used directly for teaching. Instructors save preparation time by adopting it as-is or adapting it with their own insights.4. Comprehensive Teaching Resources: The authors offer complete English-language supplementary materials, including a sample syllabus, teaching plan, ten tutorials, five assignments with solutions, and 100 additional practice problems-providing structured support for both instructors and students.