srp (version 1.2.0)

sic.l: Optimisation of the (simpler) Smooth-Rough Partition model

Description

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.

Usage

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

Arguments

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.

Value

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.

Details

Usually only called by srp.l.

See Also

sic.c, srp.l

Examples

# NOT RUN {
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")
# }