fda.usc (version 2.1.0)

optim.basis: 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,
  ...
)

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.

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.

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente

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.

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

if (FALSE) { 
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))
}