DR_sharpen {sharpPen}

Shape-Constrained Local Linear Regression via Douglas-Rachford

Description

Local linear regression is applied to bivariate data. The response is ‘sharpened’ or perturbed in a way to render a curve estimate that satisfies some specified shape constraints.

Usage

DR_sharpen(
x, y, xgrid=NULL, M=200,  h=NULL, mode=NULL, 
    ratio_1=0.14,ratio_2=0.14,ratio_3=0.14,ratio_4=0.14,
    constraint_1=NULL, constraint_2=NULL, constraint_3=NULL,
    constraint_4=NULL, norm="l2", augmentation=FALSE, maxit = 10^5)

Arguments

x

a vector of explanatory variable observations

y

binary vector of responses

xgrid

gridpoints on x-axis where estimates are taken

M

number of equally-spaced gridpoints (if xgrid not specified)

h

bandwidth

mode

the location of the peak on the x-axis, valid in the unimode case

ratio_1

control the first derivative shape constraint gap aroud the peak, valid in the unimode case

ratio_2

control the second derivative shape constraint gap aroud the peak, valid in the unimode case

ratio_3

control the third derivative shape constraint gap aroud the peak, valid in the unimode case

ratio_4

control the fourth derivative shape constraint gap aroud the peak, valid in the unimode case

constraint_1

a vector of the first derivative shape constraint

constraint_2

a vector of the second derivative shape constraint

constraint_3

a vector of the third derivative shape constraint

constraint_4

a vector of the fourth derivative shape constraint

norm

the smallest possible distance type: "l2", "l1" or "linf". Default is "l2"

augmentation

data augmentation: "TRUE" or "FALSE", default is "FALSE"

maxit

maximum iterarion number, default is 10^5

Details

Data are perturbed the smallest possible L2 or L1 or Linf distance subject to the constraint that the local linear estimate satisfies some specified shape constraints.

Value

ysharp

sharpened responses

iteration

number of iterations the function has been spend for the convergence

Author(s)

D.Wang and W.J.Braun

References

Wang, D. (2022). Penalized and constrained data sharpening methods for kernel regression (Doctoral dissertation, University of British Columbia).

Examples

set.seed(1234567)
gam<-4
g <- function(x) (3*sin(x*(gam*pi))+5*cos(x*(gam*pi))+6*x)*x
n<-100
M<-200
noise <- 1
x<-sort(runif(n,0,1))
y<-g(x)+rnorm(n,sd=noise)
z<- seq(min(x)+1/M, max(x)-1/M, length=M) ############xgrid points
h1<-dpill(x,y)
A<-lprOperator(h=h1,x=x,z=z,p=1)
local_fit<-t(A)
ss_1<-c(sign(numericalDerivative(z,g,k=1)))
DR_sharpen(x=x, y=y, xgrid=z, h=h1, constraint_1=ss_1, norm="linf",maxit =10^3)