On the use of the bootstrap for estimating functions with functional data

  • Authors:
  • Antonio Cuevas;Manuel Febrero;Ricardo Fraiman

  • Affiliations:
  • Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049-Madrid, Spain;Departamento de Estadística, Universidad de Santiago de Compostela, Spain;Departamento de Matemática, Universidad de San Andrés, Argentina

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2006

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Abstract

The bootstrap methodology for functional data and functional estimation target is considered. A Monte Carlo study analyzing the performance of the bootstrap confidence bands (obtained with different resampling methods) of several functional estimators is presented. Some of these estimators (e.g., the trimmed functional mean) rely on the use of depth notions for functional data and do not have received yet much attention in the literature. A real data example in cardiology research is also analyzed. In a more theoretical aspect, a brief discussion is given providing some insights on the asymptotic validity of the bootstrap methodology when functional data, as well as a functional parameter, are involved.