sic.c: Optimisation of the Smooth-Rough Partition model

In srp: Smooth-Rough Partitioning of the Regression Coefficients

Description

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

Usage

sic.c(x.basis = x.basis, B.basis = B.basis, x = x, y = y,
  cf0 = cf0, maxq = maxq, fixedq = F, L = L, inisp = inisp)

Arguments

x.basis	The b-spline basis defined for interpolated x in srp.c
B.basis	The b-spline basis defined for constrained regression coefficient.
x	The design matrix used in srp.c.
y	The response variable used in srp.c.
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.
L	The dimension of b-spline expansion for constrained parameters used in srp.c.
inisp	The initial value for the optimisation of tuning parameters in srp.c.

Details

Usually only called by srp.c.

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.
sp	The vector of two tuning parameters estimated by minimising generalised cross validation (GCV).
L	The number of b-spline bases used for constrained regression parameters.

Author(s)

Hyeyoung Maeng, [e-mail]

See Also

sic.l, predict.srp.c, srp.c

Examples

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"))$basis
B.basis <- create.bspline.basis(rangeval=c(0, dim(x)[1]), norder=4, nbasis=35)
result <- sic.c(x.basis=x.basis, B.basis=B.basis, x=x, y=y, cf0=ncs(x)$cf0, maxq=10, L=35, inisp=1)
plot(result$sicq, type="b")

srp documentation built on May 2, 2019, 9:31 a.m.