Statistical inference for $$L^2$$ L 2 -distances to uniformity

L. Baringhaus (), D. Gaigall () and J. P. Thiele ()
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L. Baringhaus: Leibniz Universität Hannover
D. Gaigall: Leibniz Universität Hannover
J. P. Thiele: Leibniz Universität Hannover

Computational Statistics, 2018, vol. 33, issue 4, No 13, 1863-1896

Abstract: Abstract The paper deals with the asymptotic behaviour of estimators, statistical tests and confidence intervals for $$L^2$$ 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 $$L^2$$ 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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00180-018-0820-0

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