Create Basis Set for Functional Data of fdata class

Compute basis for functional data.

Usage

create.fdata.basis(
  fdataobj,
  l = 1:5,
  maxl = max(l),
  type.basis = "bspline",
  rangeval = fdataobj$rangeval,
  class.out = "fd"
)

create.pc.basis(
  fdataobj,
  l = 1:5,
  norm = TRUE,
  basis = NULL,
  lambda = 0,
  P = c(0, 0, 1),
  ...
)

create.pls.basis(
  fdataobj,
  y,
  l = 1:5,
  norm = TRUE,
  lambda = 0,
  P = c(0, 0, 1),
  ...
)

create.raw.fdata(fdataobj, l = 1:nrow(fdataobj))

Arguments

fdataobj: fdata class object.
l: Vector of basis index.
maxl: maximum number of basis
type.basis: Type of basis (see create.basis function).
rangeval: A vector of length 2 giving the lower and upper limits of the range of permissible values for the function argument.
class.out: =="fd" basisfd class, =="fdata" fdata class.
norm: If TRUE the norm of eigenvectors basis is 1.
basis: "fd" basis object.
lambda: Amount of penalization. Default value is 0, i.e. no penalization is used.
P: If P is a vector: coefficients to define the penalty matrix object. By default P=c(0,0,1) penalize the second derivative (curvature) or acceleration. If P is a matrix: the penalty matrix object.
...: Further arguments passed to or from other methods.
y: Vector of response (scalar).

Value

basis: basis object.
x: if TRUE the value of the rotated data (the centred data multiplied by the basis matrix) is returned.
mean: functional mean of fdataobj.
df: degree of freedom.
type: type of basis.

References

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

N. Kraemer, A.-L. Boulsteix, and G. Tutz (2008). Penalized Partial Least Squares with Applications to B-Spline Transformations and Functional Data. Chemometrics and Intelligent Laboratory Systems, 94, 60 - 69. doi:10.1016/j.chemolab.2008.06.009

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es

Examples

if (FALSE) { # \dontrun{
data(tecator)
basis.pc<-create.pc.basis(tecator$absorp.fdata,c(1,4,5))
plot(basis.pc$basis,col=1)
summary(basis.pc)
basis.pls<-create.pls.basis(tecator$absorp.fdata,y=tecator$y[,1],c(1,4,5))
summary(basis.pls)
plot(basis.pls$basis,col=2)
summary(basis.pls)

basis.fd<-create.fdata.basis(tecator$absorp.fdata,c(1,4,5),
type.basis="fourier")
plot(basis.pc$basis)
basis.fdata<-create.fdata.basis(tecator$absorp.fdata,c(1,4,5),
type.basis="fourier",class.out="fdata")
plot(basis.fd,col=2,lty=1)
lines(basis.fdata,col=3,lty=1)
} # }