DeregulariseByAlpha

If possible, deregularises the input density <code>y</code> to have minimum density value is <code>alpha</code>. See details.

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

DeregulariseByAlpha function

<dl><dt>x</dt>
<dd>support of the density</dd>
<dt>y</dt>
<dd>values of the density</dd>
<dt>alpha</dt>
<dd>scalar to deregularise with (default = 0) - this will be the minimum value of the deregularised density, unless <code>min(y) &lt; alpha</code>, in which case 
no deregularisation will be performed</dd></dl>

Arguments

Function to deregularise densities to have (smaller) minimum value — DeregulariseByAlpha

<dl>

<dt>x</dt>
<dd>support of the density</dd>


<dt>y</dt>
<dd>values of the density</dd>


<dt>alpha</dt>
<dd>scalar to deregularise with (default = 0) - this will be the minimum value of the deregularised density, unless <code>min(y) &lt; alpha</code>, in which case 
no deregularisation will be performed</dd>

</dl>

DeregulariseByAlpha: Function to deregularise densities to have (smaller) minimum value

Description

Usage

Value

Arguments

Details

See Also

Examples