On an independence test approach to the goodness-of-fit problem
- Let X₁,…,Xₙ be independent and identically distributed random variables with distribution F. Assuming that there are measurable functions f:R²→R and g:R²→R characterizing a family F of distributions on the Borel sets of R in the way that the random variables f(X₁,X₂),g(X₁,X₂) are independent, if and only if F∈F, we propose to treat the testing problem H:F∈F,K:F∉F by applying a consistent nonparametric independence test to the bivariate sample variables (f(Xᵢ,Xⱼ),g(Xᵢ,Xⱼ)),1⩽i,j⩽n,i≠j. A parametric bootstrap procedure needed to get critical values is shown to work. The consistency of the test is discussed. The power performance of the procedure is compared with that of the classical tests of Kolmogorov–Smirnov and Cramér–von Mises in the special cases where F is the family of gamma distributions or the family of inverse Gaussian distributions.
| Verfasserangaben: | Ludwig Baringhaus, Daniel Gaigall |
|---|---|
| DOI: | https://doi.org/10.1016/j.jmva.2015.05.013 |
| ISSN: | 0047-259X |
| Titel des übergeordneten Werkes (Englisch): | Journal of Multivariate Analysis |
| Verlag: | Elsevier |
| Verlagsort: | Amsterdam |
| Dokumentart: | Wissenschaftlicher Artikel |
| Sprache: | Englisch |
| Erscheinungsjahr: | 2015 |
| Datum der Publikation (Server): | 16.01.2023 |
| Freies Schlagwort / Tag: | Gamma distribution; Goodness-of-fit test; Independence test; Parametric bootstrap; Vapnik–Čhervonenkis class |
| Jahrgang: | 2015 |
| Ausgabe / Heft: | 140 |
| Erste Seite: | 193 |
| Letzte Seite: | 208 |
| Link: | https://doi.org/10.1016/j.jmva.2015.05.013 |
| Zugriffsart: | weltweit |
| Fachbereiche und Einrichtungen: | FH Aachen / Fachbereich Medizintechnik und Technomathematik |
| collections: | Verlag / Elsevier |
