Abstract:
:Many techniques of functional data analysis require choosing a measure of distance between functions, with the most common choice being L2 distance. In this article we show that using a weighted L2 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. Assuming a quadratically penalized (e.g., spline) basis representation for the functional data, 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.
journal_name
Biometricsjournal_title
Biometricsauthors
Chen H,Reiss PT,Tarpey Tdoi
10.1111/biom.12161subject
Has Abstractpub_date
2014-09-01 00:00:00pages
516-25issue
3eissn
0006-341Xissn
1541-0420journal_volume
70pub_type
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