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Optimally Weighted L^2 Distance for Functional Data
Biometrics (2014)
  • Huaihou Chen
  • Philip T. Reiss
  • Thaddeus Tarpey, Wright State University
Abstract

Many techniques of functional data analysis require choosing a measure of distance between functions, with the most common choice being L^2 distance. In this paper we argue that using a weighted L^2 distance, with a judiciously chosen weight function, can improve the performance of various statistical methods for functional data, including k-medoids clustering, nonparametric classification, and permutation testing. We consider three nontrivial weight functions: design density weights, inverse-variance weights, and a new weight function that minimizes the coefficient of variation of the resulting squared distance by means of an efficient iterative procedure. The benefits of weighting, in particular with the proposed weight function, are demonstrated both in simulation studies and in applications to the Berkeley growth data and a functional magnetic resonance imaging data set.

Keywords
  • Coefficient of variation,
  • Functional classification analysis,
  • Functional clustering analysis,
  • Penalized splines,
  • Weighted L2 distance
Publication Date
September, 2014
Citation Information
Huaihou Chen, Philip T. Reiss and Thaddeus Tarpey. "Optimally Weighted L^2 Distance for Functional Data" Biometrics Vol. 70 Iss. 3 (2014)
Available at: http://works.bepress.com/phil_reiss/31/