PenS {PFLR}

Penalized B-splines Regression Model

Description

Calculates a functional regression model using the penalized B-splines method.

Usage

PenS(Y, X, alpha, M, d, domain)

Arguments

Y

Vector of length n.

X

Matrix of n x p, covariate matrix, should be dense.

alpha

Vector.

M

Integer, t1,..., tM are M equally spaced knots.

d

Integer, the degree of B-Splines.

domain

The range over which the function X(t) is evaluated and the coefficient function \beta(t) is expanded by the B-spline basis functions.

Value

beta: Estimated \beta(t) at discrete points.

extra: List containing other values which may be of use:

• b: Estimated B-spline coefficients.

• Ymean: Mean of the Y values.

• Xmean: Mean of all X values.

• Optalpha: Optimal alpha value chosen.

• M: Integer representing the number of knots used in the model calculation.

• d: Integer, degree of B-Splines used.

• domain: The range over which the function X(t) was evaluated and the coefficient function \beta(t) was expanded by the B-spline basis functions.

Examples

library(fda)
betaind = 1
snr  = 2
nsim = 1
n    = 50
p    = 21
Y = array(NA,c(n,nsim))
X = array(NA,c(n,p,nsim))
domain = c(0,1)

M = 20
d = 3
alpha = 10^(-(10:3))


for(itersim in 1:nsim)
{
dat = ngr.data.generator.bsplines(n=n,nknots=64,norder=4,p=p,domain=domain,snr=snr,betaind=betaind)
Y[,itersim]  = dat$Y
X[,,itersim] = dat$X
}

psfit = PenS(Y=Y[1:n,1],X=(X[1:n,,1]), alpha=alpha, M=M, d=d, domain=domain)