relsharpen {sharpPen}

Ridge/Enet/LASSO Sharpening via the penalty matrix.

Description

This is a data sharpening function to remove roughness, prior to use in local polynomial regression.

Usage

relsharpen(x, y, h, alpha, p=2, M=51)

Arguments

x

numeric vector of equally spaced x data. Missing values are not accepted.

y

vector of y data. Missing values are not accepted.

h

the kernel bandwidth smoothing parameter.

alpha

the elasticnet mixing parameter vector, with alpha in [0,1].

p

the order of the polynomial regression.

M

the length of the constraint points.

Details

Note that the predictor values are assumed to be equally spaced.

Value

numeric matrix of sharpened responses, with each column corresponding to different values of alpha

Author(s)

D.Wang

Examples

x<-seq(0,10,length=100)
g <- function(x) sin(x)
y<-g(x)+rnorm(100)
ys<-relsharpen(x, y, dpill(x,y), alpha=c(0.2,0.8), p=2, M=51)
y.lp2<-locpoly(x,ys[,1],bandwidth=dpill(x,y),degree=1,gridsize=100)
y.lp8<-locpoly(x,ys[,2],bandwidth=dpill(x,y),degree=1,gridsize=100)
y.lp<-locpoly(x,y,bandwidth=dpill(x,y),degree=1,gridsize=100)
curve(g,x,xlim=c(0,10))
lines(y.lp2,col=2)
lines(y.lp8,col=3)
lines(y.lp,col=5)
norm(as.matrix(g(x) - y.lp2$y),type="2")
norm(as.matrix(g(x) - y.lp8$y),type="2")
norm(as.matrix(g(x) - y.lp$y),type="2")