dens2lqd

Function for converting densities to log quantile density functions

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.

Alexander Petersen

fdadensity

Functional Data Analysis for Density Functions by Transformation
to a Hilbert Space

A. Petersen

H.G. Mueller

dens2lqd function

<dl><dt>dens</dt>
<dd>density values on dSup - must be strictly positive and integrate to 1</dd>
<dt>dSup</dt>
<dd>support (grid) for Density domain</dd>
<dt>N</dt>
<dd>desired number of points on a [0,1] grid for lqd function; default length(dSup)</dd>
<dt>lqdSup</dt>
<dd>support for lqd domain - must begin at 0 and end at 1; default [0,1] with N-equidistant support points</dd></dl>

Arguments

Function for converting densities to log quantile density functions — dens2lqd

<dl>

<dt>dens</dt>
<dd>density values on dSup - must be strictly positive and integrate to 1</dd>


<dt>dSup</dt>
<dd>support (grid) for Density domain</dd>


<dt>N</dt>
<dd>desired number of points on a [0,1] grid for lqd function; default length(dSup)</dd>


<dt>lqdSup</dt>
<dd>support for lqd domain - must begin at 0 and end at 1; default [0,1] with N-equidistant support points</dd>

</dl>

dens2lqd: Function for converting densities to log quantile density functions

Description

Usage

Value

Arguments

References

See Also

Examples