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Theory of U-Statistics

  • Book
  • © 1994

Overview

Authors:
  1. V. S. Koroljuk

    1. Institute of Mathematics, Kiev, Ukraine

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  2. Yu. V. Borovskich

    1. Institute of Textile and Light Industry, St. Petersburg, Russia

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 273)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • V. S. Koroljuk, Yu. V. Borovskich
    Pages 1-15

  3. Basic Definitions and Notions

    • V. S. Koroljuk, Yu. V. Borovskich
    Pages 17-67

  4. General Inequalities

    • V. S. Koroljuk, Yu. V. Borovskich
    Pages 69-91

  5. The Law of Large Numbers

    • V. S. Koroljuk, Yu. V. Borovskich
    Pages 93-118

  6. Weak Convergence

    • V. S. Koroljuk, Yu. V. Borovskich
    Pages 119-219

  7. Functional Limit Theorems

    • V. S. Koroljuk, Yu. V. Borovskich
    Pages 221-264

  8. Approximation in Limit Theorems

    • V. S. Koroljuk, Yu. V. Borovskich
    Pages 265-380

  9. Asymptotic Expansions

    • V. S. Koroljuk, Yu. V. Borovskich
    Pages 381-427

  10. Probabilities of Large Deviations

    • V. S. Koroljuk, Yu. V. Borovskich
    Pages 429-442

  11. The Law of Iterated Logarithm

    • V. S. Koroljuk, Yu. V. Borovskich
    Pages 443-460

  12. Dependent Variables

    • V. S. Koroljuk, Yu. V. Borovskich
    Pages 461-502

  13. Back Matter

    Pages 503-554
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Keywords

About this book

The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num­ bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc.

Authors and Affiliations

  • Institute of Mathematics, Kiev, Ukraine

    V. S. Koroljuk

  • Institute of Textile and Light Industry, St. Petersburg, Russia

    Yu. V. Borovskich

Bibliographic Information

  • Book Title: Theory of U-Statistics

  • Authors: V. S. Koroljuk, Yu. V. Borovskich

  • Series Title: Mathematics and Its Applications

  • DOI: https://doi.org/10.1007/978-94-017-3515-5

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1994

  • Hardcover ISBN: 978-0-7923-2608-3Published: 30 November 1993

  • Softcover ISBN: 978-90-481-4346-7Published: 08 December 2010

  • eBook ISBN: 978-94-017-3515-5Published: 09 March 2013

  • Edition Number: 1

  • Number of Pages: X, 554

  • Additional Information: Originally published in Russian

  • Topics: Statistical Theory and Methods, Statistics and Computing/Statistics Programs

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