Information Theory And The Central Limit Theorem

Oliver T Johnson

• Editorial: ICP
• Año: 2004
• ISBN:
  9781860945373
• Categoría: Mathematics
• Categoría: Probability & Statistics

This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems.

Índice

• Information Theory and The Central Limit Theorem
• Contents
• Preface
• 1. Introduction to Information Theory
• 2. Convergence in Relative Entropy
• 3. Non-Identical Variables and Random Vectors
• 4. Dependent Random Variables
• 5. Convergence to Stable Laws
• 6. Convergence on Compact Groups
• 7. Convergence to the Poisson Distribution
• 8. Free Random Variables
• Appendix A Calculating Entropies
• Appendix B Poincare Inequalities
• Appendix C de Bruijn Identity
• Appendix D Entropy Power Inequality
• Appendix E Relationships Between Different Forms of Convergence
• Bibliography
• Index