MakeDENsample: Convenience function for converting log quantile densities to densities

Description

See 'lqd2dens' and 'DeregulariseByAlpha' for more details. This function transforms the log quantile densities in 'qmatrix' to density functions, optionally followed by deregularisation.

Usage

MakeDENsample(
  qmatrix,
  lqdSup = seq(0, 1, length.out = ncol(qmatrix)),
  dSup = seq(0, 1, length.out = ncol(qmatrix)),
  useAlpha = FALSE,
  alpha = 0
)

Value

list with the 'DEN' transformed data, and 'dSup' that matches the input argument.

Arguments

qmatrix: Matrix holding the log quantile density values on [0,1]
lqdSup: Support grid for input log quantile densities (default = seq(0, 1, length.out = ncol(qmatrix)))
dSup: Support grid for output densities (default = seq(0, 1, length.out = ncol(qmatrix)))
useAlpha: Logical indicator to deregularise the densities (default = FALSE)
alpha: Scalar to deregularise the density - where possible, this will be the minimum value for the deregularised densities (default=0)

References

Functional Data Analysis for Density Functions by Transformation to a Hilbert space, Alexander Petersen and Hans-Georg Mueller, 2016

Examples

Run this code

 

x <- seq(0,1,length.out = 101)
# linear densities on (0, 1)
y <- t(sapply(seq(0.5, 1.5, length.out = 10), function(b) b + 2*(1 - b)*x)) 

# Get LQDs

y.lqd = MakeLQDsample(dmatrix = y, dSup = x)
matplot(y.lqd$lqdSup, t(y.lqd$LQD), ylab = 'LQD', type = 'l', lty = 1, col = 'black')

# Get Densities Back

y.dens = MakeDENsample(y.lqd$LQD, lqdSup = x, dSup = x) # should equate to y above
# These should look the same
matplot(y.dens$dSup, t(y.dens$DEN), ylab = 'Density', type = 'l', lty = 1, col = 'blue')
matplot(x, t(y), ylab = 'Original Density', type = 'l', lty = 1, col = 'red')