Minimax optimal procedures for testing the structure of multidimensional functions

John Aston, Florent Autin, Gerda Claeskens, Jean-Marc Freyermuth and Christophe Pouet

No 582277, Working Papers of Department of Decision Sciences and Information Management, Leuven from KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven

Abstract: We 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.

Keywords: Adaptation; Anisotropy; Atomic dimension; Besov spaces; Gaussian noise model; Hyperbolic wavelets; Hypothesis testing; Minimax rate; Sobol decomposition; Structural modeling (search for similar items in EconPapers)
Date: 2017-05
New Economics Papers: this item is included in nep-ecm
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Published in FEB Research Report KBI_1705

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Persistent link: https://EconPapers.repec.org/RePEc:ete:kbiper:582277

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