sic.l: Optimisation of the (simpler) Smooth-Rough Partition model
In srp: Smooth-Rough Partitioning of the Regression Coefficients

Description Usage Arguments Details Value Author(s) See Also Examples

This function performs the optimisation of the number of unconstrained regression parameters in (simpler) Smooth-Rough Partition model by minimising SIC criterion and gives the change-point in regression parameters.

1 2	sic.l(x.basis = x.basis, M.basis = M.basis, x = x, y = y, cf0 = cf0, maxq = maxq, fixedq = F)

`x.basis`	The b-spline basis defined for interpolated x in `srp.l`.
`M.basis`	The monomial basis defined for constrained regression coefficient.
`x`	The design matrix used in `srp.l`.
`y`	The response variable used in `srp.l`.
`cf0`	The coefficient matrix obtained by natural cubic spline interpolation of x in `ncs`.
`maxq`	The maximum number of unconstrained parameters if `fixedq` is FALSE. Otherwise, it is considered as a unique number of unconstrained parameters.
`fixedq`	If TRUE, `maxq` is considered as a fixed number of unconstrained parameters and if FALSE, `maxq` is a maximum and a sequence of possible values are investigated to select the optimal.

Usually only called by srp.l.

The following components are obtained only when fixedq is FALSE:

`qhat`	The optimal number of unconstrained parameters.
`sicq`	The vector of Schwarz criterion with length `maxq` which is computed for the different number of unconstrained parameters.

The following components are obtained only when fixedq is TRUE:

`muhat`	The estimator of constant parameter.
`bhat`	The vector of evaluated constrained functional regression coefficient.
`ahat`	The vector of unconstrained regression coefficient estimators.
`etahat`	The vector containing both `bhat` and `ahat` with unevaluated form.
`yhat`	The vector of estimated response variable.

Hyeyoung Maeng, h.maeng@lse.ac.uk

sic.c, srp.l

library(fda)
x <- matrix(rnorm(10000), ncol=100)
y <- matrix(rnorm(100), ncol=1)
p <- dim(x)[1] + 1
t <- seq(0, 1, length.out=dim(x)[1])*(dim(x)[1])
x.basis <- as.fd(splinefun(t, x[, 1], method="natural"))$basis
M.basis <- create.monomial.basis(rangeval=c(0, dim(x)[1]), nbasis=2)
result <- sic.l(x.basis=x.basis, M.basis=M.basis, x=x, y=y, cf0=ncs(x)$cf0, maxq=10)
plot(result$sicq, type="b")