OSCV (version 1.0)

ASE_reg: The ASE function for the local linear estimator (LLE) in the regression context.

Description

Computing \(ASE(h)\), the value of the ASE function for the local linear estimator in the regression context, for the given vector of \(h\) values.

Usage

ASE_reg(h, desx, y, rx)

Arguments

h

numerical vector of bandwidth values,

desx

numerical vecror of design points,

y

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

rx

numerical vecror of values of the regression function at \(desx\).

Value

The vector of values of \(ASE(h)\) for the correponsing vector of \(h\) values.

Details

The average squared error (ASE) is used as a measure of performace of the local linear estimator based on the Gaussian kernel.

References

Hart, J.D. and Yi, S. (1998) One-sided cross-validation. Journal of the American Statistical Association, 93(442), 620-631.

See Also

loclin, h_ASE_reg, CV_reg, OSCV_reg.

Examples

## Not run: ------------------------------------
# # Example (ASE function for a random sample of size n=100 generated from the function reg3 that
# # has six cusps. The function originates from the article of Savchuk et al. (2013).
# # The level of the added Gaussian noise is sigma=1/1000).
# n=100
# dx=(1:n-0.5)/n
# regx=reg3(dx)
# ydat=regx+rnorm(n,sd=1/1000)
# harray=seq(0.003,0.05,len=300)
# ASEarray=ASE_reg(harray,dx,ydat,regx)
# hmin=round(h_ASE_reg(dx,ydat,regx),digits=4)
# dev.new()
# plot(harray,ASEarray,'l',lwd=3,xlab="h",ylab="ASE",main="ASE function for a random sample
# from r3",cex.lab=1.7,cex.axis=1.7,cex.main=1.5)
# legend(0.029,0.0000008,legend=c("n=100","sigma=1/1000"),cex=1.7,bty="n")
# legend(0.005,0.000002,legend=paste("h_ASE=",hmin),cex=2,bty="n")
## ---------------------------------------------