Statistical Implications of Turing's Formula.

This volume features a broad introduction to recent research on Turing's formula and presents modern applications in statistics, probability, information theory and other areas of modern data science. It presents a clear introduction to Turing's formula and its connections to statistics.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Zhang, Zhiyi
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : Wiley, 2016.
Temas:
Mathematical statistics > Textbooks.
Probabilities > Textbooks.
Mathematical statistics
Probabilities
Textbooks
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Contents
  • Dedication
  • Preface
  • Chapter 1: Turing's formula
  • 1.1 Turing's Formula
  • 1.2 Univariate Normal Laws
  • 1.3 Multivariate Normal Laws
  • 1.4 Turing's formula Augmented
  • 1.5 Goodness-of
  • t by Counting Zeros
  • 1.6 Remarks
  • 1.7 Exercises
  • Chapter 2: Estimation of Simpson's indexes
  • 2.1 Generalized Simpson's indexes
  • 2.2 Estimation of Simpson's indexes
  • 2.3 Normal Laws
  • 2.4 Illustrative Examples
  • 2.5 Remarks
  • 2.6 Exercises
  • Chapter 3: Estimation of Shannon's entropy
  • 3.1 A Brief Overview
  • 3.2 The Plug-in Entropy Estimator
  • 3.2.1 When K is Finite
  • 3.2.2 When K is Countably Infinite
  • 3.3 Entropy Estimator in Turing's Perspective
  • 3.3.1 When K is Finite
  • 3.3.2 When K is Countably Infinite
  • 3.4 Appendix
  • 3.4.1 Proof of Lemma 3.2
  • 3.4.2 Proof of Lemma 3.5
  • 3.4.3 Proof of Corollary 3.5
  • 3.4.4 Proof of Lemma 3.14
  • 3.4.5 Proof of Lemma 3.18
  • 3.5 Remarks
  • 3.6 Exercises
  • Chapter 4: Estimation of Diversity indexes
  • 4.1 A Unified Perspective on Diversity indexes
  • 4.2 Estimation of Linear Diversity indexes
  • 4.3 Estimation of Renyi's Entropy
  • 4.4 Remarks
  • 4.5 Exercises
  • Chapter 5: Estimation of Information
  • 5.1 Introduction
  • 5.2 Estimation of Mutual Information
  • 5.2.1 The Plug-in Estimator
  • 5.2.2 Estimation in Turing's Perspective
  • 5.2.3 Estimation of Standardized Mutual Information
  • 5.2.4 An Illustrative Example
  • 5.3 Estimation of Kullback-Leibler Divergence
  • 5.3.1 The Plug-in Estimator
  • 5.3.2 Estimation in Turing's Perspective
  • 5.3.3 Symmetrized Kullback-Leibler Divergence
  • 5.4 Tests of Hypotheses
  • 5.5 Appendix
  • 5.5.1 Proof of Theorem 5.12
  • 5.6 Exercises
  • Chapter 6: Domains of Attraction on Countable Alphabets
  • 6.1 Introduction
  • 6.2 Domains of Attraction
  • 6.3 Examples and Remarks
  • 6.4 Appendix
  • 6.4.1 Proof of Lemma 6.3
  • 6.4.2 Proof of Theorem 6.2
  • 6.4.3 Proof of Lemma 6.6
  • 6.5 Exercises
  • Chapter 7: Estimation of Tail Probability
  • 7.1 Introduction
  • 7.2 Estimation of Pareto Tail
  • 7.3 Statistical Properties of AMLE
  • 7.4 Remarks
  • 7.5 Appendix
  • 7.5.1 Proof of Lemma 7.7
  • 7.5.2 Proof of Lemma 7.9
  • 7.6 Exercises
  • Appendix
  • Bibliography
  • Index

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