fdPar: Define a Functional Parameter Object

Description

Functional parameter objects are used as arguments to functions that estimate functional parameters, such as smoothing functions like smooth.basis. A functional parameter object is a functional data object with additional slots specifying a roughness penalty, a smoothing parameter and whether or not the functional parameter is to be estimated or held fixed. Functional parameter objects are used as arguments to functions that estimate functional parameters.

Usage

fdPar(fdobj=NULL, Lfdobj=NULL, lambda=0, estimate=TRUE,
      penmat=NULL)

Arguments

fdobj

a functional data object, functional basis object, a functional parameter object or a matrix. If it a matrix, it is replaced by fd(fdobj). If class(fdobj) == 'basisfd', it is converted to an object of class fd with a coefficient

Lfdobj

either a nonnegative integer or a linear differential operator object.

If NULL, Lfdobj depends on fdobj[['basis']][['type']]:

bspline

{ Lfdobj <- int2Lfd(max(0, norder-2)), where norder = norder(fdobj).

Value

a functional parameter object (i.e., an object of class fdPar), which is a list with the following components:
fda functional data object (i.e., with class fd)
Lfda linear differential operator object (i.e., with class Lfd)
lambdaa nonnegative real number
estimatenot currently used
penmateither NULL or a square, symmetric matrix with penmat[i, j] = integral over fd[['basis']][['rangeval']] of basis[i]*basis[j]

item

lambda
estimate
penmat

source

Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

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

Details

Functional parameters are often needed to specify initial values for iteratively refined estimates, as is the case in functions register.fd and smooth.monotone.

Often a list of functional parameters must be supplied to a function as an argument, and it may be that some of these parameters are considered known and must remain fixed during the analysis. This is the case for functions fRegress and pda.fd, for example.

Examples

Run this code

##
## Simple example
##
#  set up range for density
rangeval <- c(-3,3)
#  set up some standard normal data
x <- rnorm(50)
#  make sure values within the range
x[x < -3] <- -2.99
x[x >  3] <-  2.99
#  set up basis for W(x)
basisobj <- create.bspline.basis(rangeval, 11)
#  set up initial value for Wfdobj
Wfd0 <- fd(matrix(0,11,1), basisobj)
WfdParobj <- fdPar(Wfd0)

WfdP3 <- fdPar(seq(-3, 3, length=11))

##
##  smooth the Canadian daily temperature data
##
#    set up the fourier basis
nbasis   <- 365
dayrange <- c(0,365)
daybasis <- create.fourier.basis(dayrange, nbasis)
dayperiod <- 365
harmaccelLfd <- vec2Lfd(c(0,(2*pi/365)^2,0), dayrange)
#  Make temperature fd object
#  Temperature data are in 12 by 365 matrix tempav
#    See analyses of weather data.
#  Set up sampling points at mid days
daytime  <- (1:365)-0.5
#  Convert the data to a functional data object
daybasis65 <- create.fourier.basis(dayrange, nbasis, dayperiod)
templambda <- 1e1
tempfdPar  <- fdPar(fdobj=daybasis65, Lfdobj=harmaccelLfd,
                    lambda=templambda)

#FIXME
#tempfd <- smooth.basis(CanadianWeather$tempav, daytime, tempfdPar)$fd
#  Set up the harmonic acceleration operator
Lbasis  <- create.constant.basis(dayrange);
Lcoef   <- matrix(c(0,(2*pi/365)^2,0),1,3)
bfdobj  <- fd(Lcoef,Lbasis)
bwtlist <- fd2list(bfdobj)
harmaccelLfd <- Lfd(3, bwtlist)
#  Define the functional parameter object for
#  smoothing the temperature data
lambda   <- 0.01  #  minimum GCV estimate
#tempPar <- fdPar(daybasis365, harmaccelLfd, lambda)
#  smooth the data
#tempfd <- smooth.basis(daytime, CanadialWeather$tempav, tempPar)$fd
#  plot the temperature curves
#plot(tempfd)

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