ICV (version 1.0)

L_ICV: The ICV selection kernel.

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.

Value

The value of $L(u;\alpha,\sigma)$.

Details

The ICV selection kernel $L(u;\alpha,\sigma)=(1+\alpha)\phi(u)-\alpha\phi(u/\sigma)/\sigma$, where $\phi$ denotes the Gaussian kernel.

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

## Not run: 
# # 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)
# dev.new()
# 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)
# ## End(Not run)