統計学のための大規模標本法（テキスト・第２版）<br>Large Sample Techniques for Statistics (Springer Texts in Statistics) （2ND）

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統計学のための大規模標本法（テキスト・第２版）
Large Sample Techniques for Statistics (Springer Texts in Statistics) （2ND）

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  • 製本 Hardcover:ハードカバー版／ページ数 685 p.
  • 商品コード 9783030916947

Full Description

This book offers a comprehensive guide to large sample techniques in statistics. With a focus on developing analytical skills and understanding motivation, Large Sample Techniques for Statistics begins with fundamental techniques, and connects theory and applications in engaging ways.
The first five chapters review some of the basic techniques, such as the fundamental epsilon-delta arguments, Taylor expansion, different types of convergence, and inequalities. The next five chapters discuss limit theorems in specific situations of observational data. Each of the first ten chapters contains at least one section of case study. The last six chapters are devoted to special areas of applications. This new edition introduces a final chapter dedicated to random matrix theory, as well as expanded treatment of inequalities and mixed effects models. 
The book's case studies and applications-oriented chapters demonstrate how to use methods developed from large sample theory in real world situations. The book is supplemented by a large number of exercises, giving readers opportunity to practice what they have learned. Appendices provide context for matrix algebra and mathematical statistics. The Second Edition seeks to address new challenges in data science.
This text is intended for a wide audience, ranging from senior undergraduate students to researchers with doctorates. A first course in mathematical statistics and a course in calculus are prerequisites..

Contents

Chapter 1. The -δ Arguments.- Chapter 2. Modes of Convergence.- Chapter 3. Big O, Small o, and the Unspecified c.- Chapter 4. Asymptotic Expansions.- Chapter 5. Inequalities.- Chapter 6. Sums of Independent Random Variables.- Chapter 7. Empirical Processes.- Chapter 8. Martingales.- Chapter 9. Time and Spatial Series.- Chapter 10. Stochastic Processes.- Chapter 11. Nonparametric Statistics.- Chapter 12. Mixed Effects Models.- Chapter 13. Small-Area Estimation.- Chapter 14. Jackknife and Bootstrap.- Chapter 15. Markov-Chain Monte Carlo.- Chapter 16. Random Matrix Theory.