optim.basis: Select the number of basis using GCV method.

In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

Select the number of basis using GCV method.

Description

Functional data estimation via basis representation using cross-validation (CV) or generalized cross-validation (GCV) method with a roughness penalty.

Usage

optim.basis(
  fdataobj,
  type.CV = GCV.S,
  W = NULL,
  lambda = 0,
  numbasis = floor(seq(ncol(fdataobj)/16, ncol(fdataobj)/2, len = 10)),
  type.basis = "bspline",
  par.CV = list(trim = 0, draw = FALSE),
  verbose = FALSE,
  ...
)

Arguments

fdataobj	fdata class object.
type.CV	Type of cross-validation. By default generalized cross-validation (GCV) method.
W	Matrix of weights.
lambda	A roughness penalty. By default, no penalty lambda=0.
numbasis	Number of basis to use.
type.basis	Character string which determines type of basis. By default "bspline".
par.CV	List of parameters for type.CV: trim, the alpha of the trimming and draw=TRUE.
verbose	If TRUE information about GCV values and input parameters is printed. Default is FALSE.
...	Further arguments passed to or from other methods. Arguments to be passed by default to create.basis.

Details

Provides the least GCV for functional data for a list of number of basis num.basis and lambda values lambda. You can define the type of CV to use with the type.CV, the default is used GCV.S.

Smoothing matrix is performed by S.basis. W is the matrix of weights of the discretization points.

Value

• gcv: Returns GCV values calculated for input parameters.

• fdataobj: Matrix of set cases with dimension (n x m), where n is the number of curves and m are the points observed in each curve.

• fdata.est: Estimated fdata class object.

• numbasis.opt: numbasis value that minimizes CV or GCV method.

• lambda.opt: lambda value that minimizes CV or GCV method.

• basis.opt: basis for the minimum CV or GCV method.

• S.opt: Smoothing matrix for the minimum CV or GCV method.

• gcv.opt: Minimum of CV or GCV method.

• lambda: A roughness penalty. By default, no penalty lambda=0.

• numbasis: Number of basis to use.

• verbose: If TRUE information about GCV values and input parameters is printed. Default is FALSE.

#' @author Manuel Febrero-Bande, Manuel Oviedo de la Fuente [e-mail]

Note

min.basis deprecated.

References

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

Wasserman, L. All of Nonparametric Statistics. Springer Texts in Statistics, 2006.

Hardle, W. Applied Nonparametric Regression. Cambridge University Press, 1994.

Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. https://www.jstatsoft.org/v51/i04/

See Also

See Also as S.basis.
Alternative method: optim.np

Examples

## Not run:  
a1<-seq(0,1,by=.01)
a2=rnorm(length(a1),sd=0.2)
f1<-(sin(2*pi*a1))+rnorm(length(a1),sd=0.2)
nc<-50
np<-length(f1)
tt=1:101
S<-S.NW(tt,2)
mdata<-matrix(NA,ncol=np,nrow=50)
for (i in 1:50) mdata[i,]<- (sin(2*pi*a1))+rnorm(length(a1),sd=0.2)
mdata<-fdata(mdata)
nb<-floor(seq(5,29,len=5))
l<-2^(-5:15)
out<-optim.basis(mdata,lambda=l,numbasis=nb,type.basis="fourier")
matplot(t(out$gcv),type="l",main="GCV with fourier basis")

# out1<-optim.basis(mdata,type.CV = CV.S,lambda=l,numbasis=nb)
# out2<-optim.basis(mdata,lambda=l,numbasis=nb)

# variance calculations
y<-mdata
i<-3
z=qnorm(0.025/np)
fdata.est<-out$fdata.est
var.e<-Var.e(mdata,out$S.opt)
var.y<-Var.y(mdata,out$S.opt)
var.y2<-Var.y(mdata,out$S.opt,var.e)

# estimated fdata and point confidence interval
upper.var.e<-out$fdata.est[["data"]][i,]-z*sqrt(diag(var.e))
lower.var.e<-out$fdata.est[["data"]][i,]+z*sqrt(diag(var.e))
dev.new()
plot(y[i,],lwd=1,ylim=c(min(lower.var.e),max(upper.var.e)))
lines(out$fdata.est[["data"]][i,],col=gray(.1),lwd=1)
lines(out$fdata.est[["data"]][i,]+z*sqrt(diag(var.y)),col=gray(0.7),lwd=2)
lines(out$fdata.est[["data"]][i,]-z*sqrt(diag(var.y)),col=gray(0.7),lwd=2)
lines(upper.var.e,col=gray(.3),lwd=2,lty=2)
lines(lower.var.e,col=gray(.3),lwd=2,lty=2)
legend("top",legend=c("Var.y","Var.error"), col = c(gray(0.7),
gray(0.3)),lty=c(1,2))

## End(Not run)

fda.usc documentation built on April 4, 2025, 4:35 a.m.