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 { # }