Theory of U-Statistics

  • V. S. Koroljuk
  • Yu. V. Borovskich

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

Table of contents

  1. Front Matter
    Pages i-ix
  2. V. S. Koroljuk, Yu. V. Borovskich
    Pages 1-15
  3. V. S. Koroljuk, Yu. V. Borovskich
    Pages 17-67
  4. V. S. Koroljuk, Yu. V. Borovskich
    Pages 69-91
  5. V. S. Koroljuk, Yu. V. Borovskich
    Pages 93-118
  6. V. S. Koroljuk, Yu. V. Borovskich
    Pages 119-219
  7. V. S. Koroljuk, Yu. V. Borovskich
    Pages 221-264
  8. V. S. Koroljuk, Yu. V. Borovskich
    Pages 265-380
  9. V. S. Koroljuk, Yu. V. Borovskich
    Pages 381-427
  10. V. S. Koroljuk, Yu. V. Borovskich
    Pages 429-442
  11. V. S. Koroljuk, Yu. V. Borovskich
    Pages 443-460
  12. V. S. Koroljuk, Yu. V. Borovskich
    Pages 461-502
  13. Back Matter
    Pages 503-554

About this book

Introduction

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.

Keywords

Approximation Probability theory Random variable mathematical statistics statistics

Authors and affiliations

  • V. S. Koroljuk
    • 1
  • Yu. V. Borovskich
    • 2
  1. 1.Institute of MathematicsKievUkraine
  2. 2.Institute of Textile and Light IndustrySt. PetersburgRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-3515-5
  • Copyright Information Springer Science+Business Media B.V. 1994
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4346-7
  • Online ISBN 978-94-017-3515-5
  • About this book
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