Application of the Cramér–Wold theorem to testing for invariance under group actions

• Ricardo Fraiman ^[1] ; Leonardo Moreno ^[1] ; Thomas Ransford ^[2]
  1. [1] Universidad de la República

     Universidad de la República

     Uruguay

     
  2. [2] Laval University

     Laval University

     Canadá

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 33, Nº. 2, 2024, págs. 379-399
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We address the problem of testing for the invariance of a probability measure under the action of a group of linear transformations. We propose a procedure based on consideration of one-dimensional projections, justified using a variant of the Cramér–Wold theorem. Our test procedure is powerful, computationally efficient, and dimension-independent, extending even to the case of infinite-dimensional spaces (multivariate functional data). It includes, as special cases, tests for exchangeability and sign-invariant exchangeability. We compare our procedure with some previous proposals in these cases, in a small simulation study. The paper concludes with two real-data examples.