data_sharpening {sharpPen}

Penalized data sharpening for Local Linear, Quadratic and Cubic Regression

Description

Penalized data sharpening has been proposed as a way to enforce certain constraints on a local polynomial regression estimator. In addition to a bandwidth, a coefficient of the penalty term is also required. We propose propose systematic approaches for choosing these tuning parameters, in part, by considering the optimization problem from the perspective of ridge regression.

Usage

data_sharpening(xx,yy,zz,p,h=NULL,gammaest=NULL,penalty,lambda=NULL)

Arguments

xx

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

yy

numeric vector of y data. This must be same length as x, and missing values are not accepted.

zz

numeric vector of gridpoint z data. Missing values are not accepted.

p

degree of local polynomial used.

h

the kernel bandwidth smoothing parameter. If NULL, this value will be estimated by function dpill for Local Linear Regression, and will be estimated by function dpilc for Local Quadratic and Cubic Regression.

gammaest

the shape constraint parameter. Cannot be NULL for Periodic shape constraint. Can be NULL for Exponential shape constraint.

penalty

the type of shape constraint, can be "Exponential" and "Periodicity".

lambda

a coefficient of the penalty term, default is NULL.

Value

the sharpened response variable.

Author(s)

D.Wang and W.J.Braun

Examples

  set.seed(1234567)
  gam<-4
  gamest<-gam
  g <- function(x) 3*sin(x*(gam*pi))+5*cos(x*(gam*pi))+6*x
  sigma<-3
  xx<-seq(0,1,length=100)
  yy<-g(xx)+rnorm(100,sd=sigma)
  zz<-xx
  h1<-dpilc(xx,yy)
  local_fit<-t(lprOperator(h=h1,xx=xx,zz=zz,p=2))%*%yy
  y_sharp<-data_sharpening(xx=xx,yy=yy,zz=zz,p=2,gammaest=gamest,penalty="Periodicity")
  sharp_fit<-t(lprOperator(h=h1,xx=xx,zz=zz,p=2))%*%y_sharp
  plot(c(min(xx),max(xx)),c(min(yy)-0.5,max(yy)+0.5),type="n",,xlab="x",ylab="y")
  legend("bottomright",legend=c("curve_local","curve_sharpen"), col=c(1,3),bty="n",pch=c("-","-"))
  lines(xx,local_fit)
  lines(xx,sharp_fit,col=3, lwd=2)
  points(xx,yy,col= rgb(0.8,0.2,0.2,0.2))