Introduction to High-Dimensional Statistics, 2nd Edition

Contents

• Preface, second edition
• Preface
• Acknowledgments

1. Introduction
   • 1.1   High-Dimensional Data
   • 1.2   Curse of Dimensionality
   • 1.2.1   Lost in the Immensity of High-Dimensional Spaces
   • 1.2.2   Fluctuations Cumulate
   • 1.2.3   Accumulation of Rare Events May Not Be Rare
   • 1.2.4   Computational Complexity
   • 1.3   High-Dimensional Statistics
   • 1.3.1   Circumventing the Curse of Dimensionality
   • 1.3.2   A Paradigm Shift
   • 1.3.3   Mathematics of High-Dimensional Statistics
   • 1.4   About This Book
   • 1.4.1   Statistics and Data Analysis
   • 1.4.2   Purpose of This Book
   • 1.4.3   Overview
   • 1.5   Discussion and References
   • 1.5.1   Take-Home Message
   • 1.5.2   References
   • 1.6   Exercises
   • 1.6.1   Strange Geometry of High-Dimensional Spaces
   • 1.6.2   Volume of a p-Dimensional Ball ...