relsharp_linear {sharpPen}

Ridge/Enet/LASSO Sharpening via the linear regression.

Description

This is a function to shrink responses towards their estimations of linear regression as a form of data sharpening to remove roughness, prior to use in local polynomial regression.

Usage

 relsharp_linear(x, y, alpha) 

Arguments

x

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

y

vector of y data. Missing values are not accepted.

alpha

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

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<-relsharp_linear(x, y,alpha=c(0.2,0.8))
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")