The Methods of Distances in the Theory of Probability and Statistics

  • Svetlozar T. Rachev
  • Lev B. Klebanov
  • Stoyan V. Stoyanov
  • Frank Fabozzi

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
    Pages 1-7
  3. General topics in the theory of probability metrics

    1. Front Matter
      Pages 9-9
    2. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 11-31
    3. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 33-66
    4. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 67-105
  4. Relations between compound, simple and primary distances

    1. Front Matter
      Pages 107-107
    2. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 109-143
    3. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 145-167
    4. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 169-197
    5. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 199-217
    6. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 219-233
  5. Applications of minimal probability distances

    1. Front Matter
      Pages 235-235
    2. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 237-270
    3. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 271-282
    4. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 283-296
    5. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 297-315
    6. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 317-331
  6. Ideal metrics

    1. Front Matter
      Pages 333-333
    2. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
      Pages 335-362

About this book

Introduction

This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to study stability problems and reduces to  the selection of an ideal or the most appropriate metric for the problem under consideration and a comparison of probability metrics.

After describing the basic structure of probability metrics and providing an analysis of the topologies in the space of probability measures generated by different types of probability metrics, the authors study stability problems by providing a characterization of the ideal metrics for a given problem and investigating the main relationships between different types of probability metrics. The presentation is provided in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases.

      Svetlozar T.  Rachev is the Frey Family Foundation Chair of Quantitative Finance, Department of Applied Mathematics and Statistics, SUNY-Stony Brook  and Chief Scientist of Finanlytica, USA. Lev B. Klebanov is a Professor in the Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic. Stoyan V. Stoyanov is a Professor at EDHEC Business School and Head of Research, EDHEC-Risk Institute—Asia (Singapore).  Frank J. Fabozzi is a Professor at EDHEC Business School. (USA)

 

Keywords

Monge-Kantorovich mass transference problem Probability distances Statistical parameter estimation Theory of Probability Distances

Authors and affiliations

  • Svetlozar T. Rachev
    • 1
  • Lev B. Klebanov
    • 2
  • Stoyan V. Stoyanov
    • 3
  • Frank Fabozzi
    • 4
  1. 1.Inst. Statistik und Mathematische, WirtschaftstheorieUniversität KarlsruheKarlsruheGermany
  2. 2., Department of Probability and StatisticsCharles UniversityPragueCzech Republic
  3. 3., EDHEC-Risk InstituteEDHEC Business SchoolSingaporeSingapore
  4. 4.New HopeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-4869-3
  • Copyright Information Springer Science+Business Media, LLC 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-4868-6
  • Online ISBN 978-1-4614-4869-3
  • About this book