Symmetric Statistics

  • Rabi Bhattacharya
  • Manfred Denker
Part of the DMV Seminar book series (OWS, volume 14)


This chapter deals with principles of the asymptotic distribution theory for symmetric statistics, that are U-statistics, differentiable statistical functions and certain multiple stochastic integrals. Since the multiple sample case is delt with in a quite similar way, we can restrict attention to the classical one-sample statistics. General references are [D1], [RW] and [S1] among many other books. The first one contains some technical material needed to fill in details of the following discussion. It is also helpful to understand the little changes necessary in the multisample case.


Invariance Principle Empirical Process Iterate Logarithm Empirical Distribution Function Symmetric Statistic 
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Copyright information

© Birkhäuser Verlag Basel 1990

Authors and Affiliations

  • Rabi Bhattacharya
    • 1
  • Manfred Denker
    • 2
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Institut für MathematischeStochastikGöttingenGermany

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