L_ICV: The ICV selection kernel.

In osavchuk/ICV: Indirect cross-validation (ICV) for kernel density estimation

Description

The ICV selection kernel L defined by expression (4) of Savchuk, Hart, and Sheather (2010).

Usage

L_ICV(u, alpha, sigma)

Arguments

u	numerical argument of the selection kernel,
alpha	first parameter of the selection kernel,
sigma	second parameter of the selection kernel.

Details

The ICV selection kernel L(u;α,σ)=(1+α)φ(u)-αφ(u/σ)/σ, where φ denotes the Gaussian kernel.

Value

The value of L(u;α,σ).

References

Savchuk, O.Y., Hart, J.D., Sheather, S.J. (2010). Indirect cross-validation for density estimation. Journal of the American Statistical Association, 105(489), 415-423.

See Also

ICV, h_ICV, C_ICV, MISE_mixnorm, KDE_ICV, LocICV.

Examples

# Graph of the ICV selection kernel with (alpha,sigma)=(2.42,5.06).
u=seq(-10,10,len=1000)
kern=L_ICV(u,2.42,5.06)
X11()
plot(u,kern,'l',lwd=2,ylim=c(-0.2,1.2),ylab="kernel",cex.lab=1.7,cex.axis=1.7,main="")
lines(u,dnorm(u),lwd=3,lty="dashed")
title(main="Selection kernel with (alpha,sigma)=(2.42,5.06)",cex.main=1.6)
legend(-11, 1.2, legend=c("ICV kernel","Gaussian kernel"),lwd=c(3,3),lty=c(1,2),bty="n",cex=1.3)

osavchuk/ICV documentation built on May 24, 2019, 3:59 p.m.