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Keywords
- likelihood ratio test (2)
- Bahadur efficiency (1)
- Bootstrapping (1)
- Collective risk model (1)
- Coverage probability (1)
- Equivalence test (1)
- Gamma distribution (1)
- Goodness-of-fit test (1)
- Goodness-of-fit tests for uniformity (1)
- Hotelling’s T² test (1)
- Independence test (1)
- Integrated empirical distribution (survival) function (1)
- Kernel density estimator (1)
- Length of confidence intervals (1)
- Numerical inversion of Laplace transforms (1)
- Parametric bootstrap (1)
- Pitman efficiency (1)
- Vapnik–Čhervonenkis class (1)
- Volume of confidence regions (1)
- Wilcoxon tests (1)
The paper deals with the asymptotic behaviour of estimators, statistical tests and confidence intervals for L²-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 L²-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.