crossval: Leave-one-out cross-validation
In funcreg: Functional Regression Estimation

Description Usage Arguments Value References Examples

It computes the cross-validation for a given lambda and k or find the optimal lambda for a given k (see below).

funcregCV(form, create_basis=create.bspline.basis, LD=2, lambda,
          k, CstInt=FALSE, regularized=TRUE, alpha=1e-5, data=NULL,
          obj=NULL, ...)

getFuncregLam(form, create_basis=create.bspline.basis, LD=2, lam0,
              k, regularized=TRUE, CstInt=FALSE, data=NULL, loglam=FALSE,
              method="BFGS", alpha=1e-5, optimArg=list(), ...)

`obj`	An object of class "funcreg". If `NULL`, all other arguments must be set.
`form`	A formula for the functional regression. Arguments are objects of class "myfda" obtained either by `coefEst` or `nlCoefEst`, and must be in the local environment.
`create_basis`	The function used to create the basis object (see `create.bspline.basis`) for the functional parameters.
`LD`	Either a nonnegative integer defining an order of a derivative or a linear differential operator (see `eval.penalty`).
`data`	An optional list of `myfda` objects, which are the functional data included in the formula `form`
`lambda`	A vector of regularization parameters that penalizes for the absence of smoothness. The dimention is 2 times the number of regressors plus 1 if there is an intercept and if `CstInt=FALSE`. The first is for the intercept, the second and third for the first regressor and so on. If it is a scalar, it is assumed that the smoothing parameter is the same for all functional parameters.
`lam0`	Initial value of lambda for the minimization of the cross-validation
`k`	A vector of integers representing the number of basis for each functional parameter. The first is for the intercept (if there is an intercept and that `Cstint=FALSE`), the second for the first functional parameter and so on. If it is a scalar, it is assumed that the number of basis is the same for all functional parameters.
`regularized`	If `TRUE`, the system is regularized by add `alpha` to the main diagonal of the regression matrix
`CstInt`	If `TRUE`, the intercept is assumed constant. If `FALSE`, it is a one dimensional functional parameter.
`loglam`	If `TRUE`, lam0 is `log10(lambda)` and the function minimizes `CV(10^lam)`. It prevents the lambda's from being negative.
`method`	The algorithm used by `link{optim}`
`optimArg`	A list of additional arguments to pass to `link{optim}`
`alpha`	The regularization parameter. The value is added to the diagonal of the regression matrix to make sure it is positive definite.
`...`	Additional arguments to be passed to `create_basis` (see `create.bspline.basis`).

'funregCV' returns the value of the leave-one-out cross-validation. The attributes 'convergence', returns convergence code for each estimation.

'getFuncregLam' returns the fitted object of class 'funcreg' using the optimal lambda. The argument 'optimRes' gives the optim output from the minimization of the cross-validation.

Ramsay, James O., & Silverman, Bernard W. (2005), Functional Data Analysis, Springer, New York.

data(GDPv56) 

## We just create response and a covariate artificialy from the GDP
## series

y <- GDPv56[,1:30]
x <- GDPv56[,31:60]
t <- seq(0,1,len=nrow(y))

## First we create the "myfda" objects
yfd <- coefEst(y, t, .0004, 15, 2)
xfd <- coefEst(x, t, .0004, 15, 2)


## with the object
res <- funcreg(yfd~xfd, k=c(5,5), lambda=c(.001,.001,.001))
funcregCV(obj=res)

## without object
funcregCV(yfd~xfd, k=c(5,5), lambda=c(.001,.001,.001))

## With the default values
getFuncregLam(yfd~xfd, k=c(5,5), lam0=c(.001,.001,.001))

## With upper and lower bound
getFuncregLam(yfd~xfd, k=c(5,5), lam0=c(.001,.001,.001), method="L-BFGS-B",
             optimArg=list(lower=c(0,0,0),upper=c(200,200,200))) 

## With loglam
res <- getFuncregLam(yfd~xfd, k=c(5,5), lam0=c(-3,-3,-3), loglam=TRUE)
res

## Get info about the optim()
res$optimRes