RELsharpening {sharpPen}

Ridge/Enet/LASSO Sharpening via the mean/local polynomial regression with large bandwidth/linear regression.

Description

This is a function to shrink responses towards their mean/estimations of local polynomial regression with large bandwidth/estimations of linear regression as a form of data sharpening to remove roughness, and reduce the bias (when "combine=TRUE"), prior to use in local polynomial regression.

Usage

RELsharpening(x,y,alpha,type,bigh,hband,combine)

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].

type

The type of the base line. In total, we have three types: "mean", "big_h", and "linear".

bigh

the kernel bandwidth smoothing parameter.

hband

the kernel bandwidth smoothing parameter, which will be used in the residual sharpening method.

combine

Should the smoother combined with residual method or not, default=FALSE.

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<-RELsharpening(x, y,alpha=c(0.2,0.8),"big_h", dpill(x,y)*4, dpill(x,y),combine=TRUE)
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")