Functional data estimation via basis representation using cross-validation (CV) or generalized cross-validation (GCV) method with a roughness penalty.
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,
...
)fdata class object.
Type of cross-validation. By default generalized cross-validation (GCV) method.
Matrix of weights.
A roughness penalty. By default, no penalty lambda=0.
Number of basis to use.
Character string which determines type of basis. By default "bspline".
List of parameters for type.CV: trim, the alpha of the
trimming and draw=TRUE.
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.
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.
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.
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. http://www.jstatsoft.org/v51/i04/
# 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))
# }
# NOT RUN {
# }