Variable-dependent partial dimension reduction

• Lu Li ^[1] ; Kai Tan ^[4] ; Xuerong Meggie Wen ^[2] ; Zhou Yu ^[3]
  1. [1] Shanghai Jiao Tong University

     Shanghai Jiao Tong University

     China

     
  2. [2] Missouri University of Science and Technology

     Missouri University of Science and Technology

     Township of Rolla, Estados Unidos

     
  3. [3] East China Normal University

     East China Normal University

     China

     
  4. [4] The State University of New Jersey

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 32, Nº. 2, 2023, págs. 521-541
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Sufficient dimension reduction reduces the dimension of a regression model without loss of information by replacing the original predictor with its lower-dimensional linear combinations. Partial (sufficient) dimension reduction arises when the predictors naturally fall into two sets X and W, and pursues a partial dimension reduction of X. Though partial dimension reduction is a very general problem, only very few research results are available when W is continuous. To the best of our knowledge, none can deal with the situation where the reduced lower-dimensional subspace of Xvaries with W. To address such issue, we in this paper propose a novel variable-dependent partial dimension reduction framework and adapt classical sufficient dimension reduction methods into this general paradigm. The asymptotic consistency of our method is investigated. Extensive numerical studies and real data analysis show that our variable-dependent partial dimension reduction method has superior performance compared to the existing methods.