OSCV (version 1.0)

loclin: Computing the local linear estimate (LLE).

Description

Computing the LLE based on data \((desx,y)\) over the given vector of the argument values \(u\). The Gausssian kernel is used. See expression (3) in Savchuk and Hart (2017).

Usage

loclin(u, desx, y, h)

Arguments

u

numerical vector of argument values,

desx

numerical vecror of design points,

y

numerical vecror of data values (corresponding to the specified design points \(desx\)),

h

numerical bandwidth value (scalar).

Value

Numerical vector of the LLE values computed over the specified vector of \(u\) points.

Details

Computing the LLE based on the Gaussian kernel for the specified vector of the argument values \(u\) and given vectors of design points \(desx\) and the corresponding data values \(y\).

References

• Clevelend, W.S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74(368), 829-836.
• 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.

See Also

OSCV_reg, h_OSCV_reg, ASE_reg, h_ASE_reg, CV_reg.

Examples

## Not run: ------------------------------------
# # Example (simulated data).
# n=200
# dx=(1:n-0.5)/n
# regf=2*dx^10*(1-dx)^2+dx^2*(1-dx)^10
# u=seq(0,1,len=1000)
# ydat=regf+rnorm(n,sd=0.002)
# dev.new()
# plot(dx,regf,'l',lty="dashed",lwd=3,xlim=c(0,1),ylim=c(1.1*min(ydat),1.1*max(ydat)),
# cex.axis=1.7,cex.lab=1.7)
# title(main="Function, generated data, and LLE",cex.main=1.5)
# points(dx,ydat,pch=20,cex=1.5)
# lines(u,loclin(u,dx,ydat,0.05),lwd=3,col="blue")
# legend(0,1.1*max(ydat),legend=c("LLE based on h=0.05","true regression function"),
# lwd=c(2,3),lty=c("solid","dashed"),col=c("blue","black"),cex=1.5,bty="n")
# legend(0.7,0.5*min(ydat),legend="n=200",cex=1.7,bty="n")
## ---------------------------------------------