Abstract.
In this paper we provide conditions under which a distribution is determined by just one randomly chosen projection. Thenweapply our results to construct goodness-of-fit tests for the one and two-sample problems. We include some simulations as well as the application of our results to a real data set. Our results are valid for every separable Hilbert space.
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*Partially supported by the Spanish Ministerio de Ciencia y Tecnología, grant MTM2005-08519-C02-02.
**Partially supported by grants from NSERC and the Canada research chairs program.
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Cuesta-Albertos*, J.A., Fraiman, R. & Ransford**, T. Random projections and goodness-of-fit tests in infinite-dimensional spaces. Bull Braz Math Soc, New Series 37, 477–501 (2006). https://doi.org/10.1007/s00574-006-0023-0
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DOI: https://doi.org/10.1007/s00574-006-0023-0
Keywords:
- Cramér-Wold theorem
- random projections
- Hilbert spaces
- goodness-of-fit tests
- Kolmogorov-Smirnov projected test
- single null hypothesis
- two samples