fdadensity: Functional Data Analysis for Density Functions by Transformation
to a Hilbert Space
An implementation of the methodology described in
Petersen and Mueller (2016) <doi:10.1214/15-AOS1363> for the functional
data analysis of samples of density functions. Densities are first
transformed to their corresponding log quantile densities, followed by
ordinary Functional Principal Components Analysis (FPCA). Transformation
modes of variation yield improved interpretation of the variability in the
data as compared to FPCA on the densities themselves. The standard
fraction of variance explained (FVE) criterion commonly used for functional
data is adapted to the transformation setting, also allowing for an
alternative quantification of variability for density data through the
Wasserstein metric of optimal transport.
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