Cramér–von Mises distance: probabilistic interpretation, confidence intervals, and neighbourhood-of-model validation
| Autor: | Ludwig Baringhaus, Norbert Henze |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
010102 general mathematics Probabilistic logic Neighbourhood (graph theory) 01 natural sciences Confidence interval Interpretation (model theory) Model validation 010104 statistics & probability Distribution function Cramér–von Mises criterion Statistics Applied mathematics 0101 mathematics Statistics Probability and Uncertainty Value (mathematics) Mathematics |
| Zdroj: | Journal of Nonparametric Statistics. 29:167-188 |
| ISSN: | 1029-0311 1048-5252 |
| Popis: | We give a probabilistic interpretation of the Cramer–von Mises distance between continuous distribution functions F and . If F is unknown, we construct an asymptotic confidence interval for based on a random sample from F. Moreover, for given and some value , we propose an asymptotic equivalence test of the hypothesis that against the alternative . If such a ‘neighbourhood-of- validation test’, carried out at a small asymptotic level, rejects the hypothesis, there is evidence that F is within a distance of . As a neighbourhood-of-exponentiality test shows, the method may be extended to the case that is composite. |
| Databáze: | OpenAIRE |
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