Details
| Original language | English |
|---|---|
| Pages (from-to) | 1863 - 1896 |
| Number of pages | 34 |
| Journal | Computational Statistics and Data Analysis |
| Volume | 33 |
| Issue number | 4 |
| Early online date | 22 May 2018 |
| Publication status | Published - Dec 2018 |
Abstract
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.
Keywords
- Coverage probability, Equivalence test, Goodness-of-fit tests for uniformity, Integrated empirical distribution (survival) function, Neighbourhood-of-uniformity validation test, Numerical inversion of Laplace transforms
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Computational Statistics and Data Analysis, Vol. 33, No. 4, 12.2018, p. 1863 - 1896.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Statistical inference for L2-distances to uniformity
AU - Baringhaus, Ludwig
AU - Gaigall, Daniel
AU - Thiele, Jan Philipp
PY - 2018/12
Y1 - 2018/12
N2 - 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.
AB - 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.
KW - Coverage probability
KW - Equivalence test
KW - Goodness-of-fit tests for uniformity
KW - Integrated empirical distribution (survival) function
KW - Neighbourhood-of-uniformity validation test
KW - Numerical inversion of Laplace transforms
UR - http://www.scopus.com/inward/record.url?scp=85053006846&partnerID=8YFLogxK
U2 - 10.1007/s00180-018-0820-0
DO - 10.1007/s00180-018-0820-0
M3 - Article
VL - 33
SP - 1863
EP - 1896
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
SN - 0167-9473
IS - 4
ER -