Computational Statistics

, Volume 33, Issue 4, pp 1863–1896 | Cite as

Statistical inference for \(L^2\)-distances to uniformity

  • L. BaringhausEmail author
  • D. Gaigall
  • J. P. Thiele
Original Paper


The paper deals with the asymptotic behaviour of estimators, statistical tests and confidence intervals for \(L^2\)-distances to uniformity based on the empirical distribution function, the integrated empirical distribution function and the integrated empirical survival function. Approximations of power functions, confidence intervals for the \(L^2\)-distances and statistical neighbourhood-of-uniformity validation tests are obtained as main applications. The finite sample behaviour of the procedures is illustrated by a simulation study.


Integrated empirical distribution (survival) function Goodness-of-fit tests for uniformity Numerical inversion of Laplace transforms Coverage probability Equivalence test Neighbourhood-of-uniformity validation test 



The authors thank the referees for constructive comments and suggestions.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für Mathematische StochastikLeibniz Universität HannoverHannoverGermany
  2. 2.Institut für Angewandte MathematikLeibniz Universität HannoverHannoverGermany

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