fda (version 6.1.8)

smooth.fd: Smooth a Functional Data Object Using an Indirectly Specified Roughness Penalty

Description

Smooth data already converted to a functional data object, fdobj, using criteria consolidated in a functional data parameter object, fdParobj. For example, data may have been converted to a functional data object using function smooth.basis using a fairly large set of basis functions. This 'fdobj' is then smoothed as specified in 'fdParobj'.

Usage

smooth.fd(fdobj, fdParobj)

Value

a functional data object.

Arguments

fdobj

a functional data object to be smoothed.

fdParobj

a functional parameter object. This object is defined by a roughness penalty in slot Lfd and a smoothing parameter lambda in slot lambda, and this information is used to further smooth argument fdobj.

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

smooth.basis,

Examples

oldpar <- par(no.readonly=TRUE)
#  Shows the effects of two levels of smoothing
#  where the size of the third derivative is penalized.
#  The null space contains quadratic functions.
x <- seq(-1,1,0.02)
y <- x + 3*exp(-6*x^2) + rnorm(rep(1,101))*0.2
#  set up a saturated B-spline basis
basisobj <- create.bspline.basis(c(-1,1),81)
#  convert to a functional data object that interpolates the data.
result <- smooth.basis(x, y, basisobj)
yfd  <- result$fd

#  set up a functional parameter object with smoothing
#  parameter 1e-6 and a penalty on the 3rd derivative.
yfdPar <- fdPar(yfd, 2, 1e-6)
yfd1 <- smooth.fd(yfd, yfdPar)

#. this code throws an error for. non-cran check
# if (!CRAN()) {
# FIXME: using 3rd derivative here gave error?????
# yfdPar3 <- fdPar(yfd, 3, 1e-6)
# yfd1.3 <- smooth.fd(yfd, yfdPar3)
# Error in bsplinepen(basisobj, Lfdobj, rng) :
#	Penalty matrix cannot be evaluated
#  for derivative of order 3 for B-splines of order 4
# }

#  set up a functional parameter object with smoothing
#  parameter 1 and a penalty on the 3rd derivative.
yfdPar <- fdPar(yfd, 2, 1)
yfd2 <- smooth.fd(yfd, yfdPar)
#  plot the data and smooth
plot(x,y)           # plot the data
lines(yfd1, lty=1)  #  add moderately penalized smooth
lines(yfd2, lty=3)  #  add heavily  penalized smooth
legend(-1,3,c("0.000001","1"),lty=c(1,3))
#  plot the data and smoothing using function plotfit.fd
plotfit.fd(y, x, yfd1)  # plot data and smooth
par(oldpar)