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Non-Parametric Statistical Diagnosis

Problems and Methods

  • B. E. Brodsky
  • B. S. Darkhovsky

Part of the Mathematics and Its Applications book series (MAIA, volume 509)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Theory

    1. Front Matter
      Pages 1-1
    2. B. E. Brodsky, B. S. Darkhovsky
      Pages 3-82
    3. B. E. Brodsky, B. S. Darkhovsky
      Pages 83-126
    4. B. E. Brodsky, B. S. Darkhovsky
      Pages 219-297
    5. B. E. Brodsky, B. S. Darkhovsky
      Pages 299-329
  3. Applications

    1. Front Matter
      Pages 331-331
    2. B. E. Brodsky, B. S. Darkhovsky
      Pages 389-406
  4. Back Matter
    Pages 407-452

About this book

Introduction

This book has a distinct philosophy and it is appropriate to make it explicit at the outset. In our view almost all classic statistical inference is based upon the assumption (explicit or implicit) that there exists a fixed probabilistic mechanism of data generation. Unlike classic statistical inference, this book is devoted to the statistical analysis of data about complex objects with more than one probabilistic mechanism of data generation. We think that the exis­ tence of more than one data generation process (DGP) is the most important characteristic of com plex systems. When the hypothesis of statistical homogeneity holds true, Le., there exists only one mechanism of data generation, all statistical inference is based upon the fundamentallaws of large numbers. However, the situation is completely different when the probabilistic law of data generation can change (in time or in the phase space). In this case all data obtained must be 'sorted' in subsamples generated by different probabilistic mechanisms. Only after such classification we can make correct inferences about all DGPs. There exists yet another type of problem for complex systems. Here it is important to detect possible (but unpredictable) changes of DGPs on-line with data collection. Since the complex system can change the probabilistic mechanism of data generation, the correct statistical analysis of such data must begin with decisions about possible changes in DGPs.

Keywords

biology diagnosis diagnostics econometrics statistics

Authors and affiliations

  • B. E. Brodsky
    • 1
  • B. S. Darkhovsky
    • 2
  1. 1.Higher School of EconomicsState UniversityMoscowRussia
  2. 2.Institute for Systems AnalysisRussian Academy of SciencesMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9530-8
  • Copyright Information Springer Science+Business Media B.V. 2000
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5465-4
  • Online ISBN 978-94-015-9530-8
  • Buy this book on publisher's site
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