Functional Data Analysis for Density Functions by Transformation to a Hilbert Space
Transformation Mode of Variation Plot
Function for converting densities to log quantile density functions
Function for converting Densities to Quantile Densities
Function for converting Densities to Quantile Functions
Function to deregularise densities to have (smaller) minimum value
FPCA for densities by log quantile density transformation
Compute Metric-based Fraction of Variance Explained
Wasserstein Frechet Mean Computation
Function for converting log quantile densities to densities
Function for converting log quantile densities to quantile functions
Convenience function for converting log quantile densities to densitie...
Convenience function for converting densities to log-quantile densitie...
Normalise Densities
Function for converting Quantile Densities to Densities
Function to regularise densities to have (larger) minimum value
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.