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dc.contributor.authorArias-Castro, Eryen_US
dc.contributor.authorPelletier, Brunoen_US
dc.contributor.authorSaligrama, Venkateshen_US
dc.date.accessioned2018-06-19T16:20:02Z
dc.date.available2018-06-19T16:20:02Z
dc.date.issued2018
dc.identifier.citationEry Arias-Castro, Bruno Pelletier & Venkatesh Saligrama (2018) Remember the curse of dimensionality: the case of goodness-of-fit testing in arbitrary dimension, Journal of Nonparametric Statistics, 30:2, pp. 448-471, https://doi.org/10.1080/10485252.2018.1435875
dc.identifier.urihttps://hdl.handle.net/2144/29422
dc.description.abstractDespite a substantial literature on nonparametric two-sample goodness-of-fit testing in arbitrary dimensions, there is no mention there of any curse of dimensionality. In fact, in some publications, a parametric rate is derived. As we discuss below, this is because a directional alternative is considered. Indeed, even in dimension one, Ingster, Y. I. [(1987). Minimax testing of nonparametric hypotheses on a distribution density in the l_p metrics. Theory of Probability & Its Applications, 31(2), 333–337] has shown that the minimax rate is not parametric. In this paper, we extend his results to arbitrary dimension and confirm that the minimax rate is not only nonparametric, exhibits but also a prototypical curse of dimensionality. We further extend Ingster's work to show that the chi-squared test achieves the minimax rate. Moreover, we show that the test adapts to the intrinsic dimensionality of the data. Finally, in the spirit of Ingster, Y. I. [(2000). Adaptive chi-square tests. Journal of Mathematical Sciences, 99(2), 1110–1119], we consider a multiscale version of the chi-square test, showing that one can adapt to unknown smoothness without much loss in power.en_US
dc.format.extent1 - 24en_US
dc.publisherTaylor & Francisen_US
dc.relation.ispartofJournal of Nonparametric Statistics
dc.subjectStatistics theoryen_US
dc.subjectMathematicsen_US
dc.subjectStatisticsen_US
dc.subjectEconometricsen_US
dc.subjectStatistics & probabilityen_US
dc.titleRemember the curse of dimensionality: the case of goodness-of-fit testing in arbitrary dimensionen_US
dc.typeArticleen_US
dc.identifier.doi10.1080/10485252.2018.1435875
pubs.elements-sourcemanual-entryen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Engineeringen_US
pubs.organisational-groupBoston University, College of Engineering, Department of Electrical & Computer Engineeringen_US


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