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Minimax optimal procedures for testing the structure of multidimensional functions

dc.creatorAston, John Alexander
dc.creatorAutin, F
dc.creatorClaeskens, G
dc.creatorFreyermuth, J-M
dc.creatorPouet, C
dc.date.accessioned2017-05-01
dc.date.accessioned2018-11-24T23:27:28Z
dc.date.available2017-08-17T15:55:02Z
dc.date.available2018-11-24T23:27:28Z
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/266590
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3987
dc.description.abstractWe present a novel method for detecting some structural characteristics of multidimensional functions. We consider the multidimensional Gaussian white noise model with an anisotropic estimand. Using the relation between the Sobol decomposition and the geometry of multidimensional wavelet basis we can build test statistics for any of the Sobol functional components. We assess the asymptotical minimax optimality of these test statistics and show that they are optimal in presence of anisotropy with respect to the newly determined minimax rates of separation. An appropriate combination of these test statistics allows to test some general structural characteristics such as the atomic dimension or the presence of some variables. Numerical experiments show the potential of our method for studying spatio-temporal processes.
dc.languageen
dc.publisherElsevier
dc.publisherApplied and Computational Harmonic Analysis
dc.rightshttp://creativecommons.org/licenses/by/4.0/
dc.rightsAttribution 4.0 International
dc.subjectadaptation
dc.subjectanisotropy
dc.subjectatomic dimension
dc.subjectBesov spaces
dc.subjectGaussian noise model
dc.subjecthyperbolic wavelets
dc.subjecthypothesis testing
dc.subjectminimax rate
dc.subjectSobol decomposition
dc.subjectstructural modeling
dc.titleMinimax optimal procedures for testing the structure of multidimensional functions
dc.typeArticle


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