reg3 {OSCV}

Nonsmooth regression function with six cusps.

Description

Nonsmooth regression function r_3 with six cusps used in the simulation studies in Savchuk et al. (2013) and Savchuk et al. (2017).

Usage

reg3(u)

Arguments

u

numerical vecror of argument values in the range [0,1].

Details

The nonsmooth function r_3 can be used in simulation studies.

Value

The vector of values of r_3 corresponding to the values of the vector u.

References

• Savchuk, O.Y., Hart, J.D., Sheather, S.J. (2013). One-sided cross-validation for nonsmooth regression functions. Journal of Nonparametric Statistics, 25(4), 889-904.

• Savchuk, O.Y., Hart, J.D. (2017). Fully robust one-sided cross-validation for regression functions. Computational Statistics, doi:10.1007/s00180-017-0713-7.

Examples

## Not run: 
# n=250 data points are generated from r3 by adding the Gaussian noise with sigma=1/500.
# The fixed evenly spaced design is used.
u=seq(0,1,len=1000)
n=250
xdat=(1:n-0.5)/n
ydat=reg3(xdat)+rnorm(n,sd=1/500)
h_oscv=round(h_OSCV_reg(xdat,ydat,1),digits=4) # L_G-based OSCV based on nonsmooth constant
l=loclin(u,xdat,ydat,h_oscv)
dev.new()
plot(xdat,ydat,pch=20,cex=1.5,cex.axis=1.5,cex.lab=1.5,xlab="x",ylab="y",
ylim=c(min(ydat),1.2*max(ydat)))
lines(u,l,'l',lwd=3,col="blue")
lines(u,reg3(u),lwd=3,lty="dashed")
title(main="Data, true regression function and LLE",cex.main=1.7)
legend(-0.05,0.003,legend=paste("h_OSCV=",h_oscv),cex=2,bty="n")
legend(0.65,0.025, legend="n=250",cex=2,bty="n")
legend(0,1.28*max(ydat),legend=c("LLE based on h_OSCV","true regression function"),lwd=c(3,3),
lty=c("solid","dashed"),col=c("blue","black"),bty="n",cex=1.5)

## End(Not run)