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Minimax optimal procedures for testing the structure of multidimensional functions

Author

Listed:
  • John Aston
  • Florent Autin
  • Gerda Claeskens
  • Jean-Marc Freyermuth
  • Christophe Pouet

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.

Suggested Citation

  • John Aston & Florent Autin & Gerda Claeskens & Jean-Marc Freyermuth & Christophe Pouet, 2017. "Minimax optimal procedures for testing the structure of multidimensional functions," Working Papers of Department of Decision Sciences and Information Management, Leuven 582277, KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven.
    • Handle: RePEc:ete:kbiper:582277
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