ISE_fstar {OSCV}

The ISE function in the kernel density estimation (KDE) context in the case when the underlying density is fstar.

Description

Computing the ISE function for the Gaussian density estimator obtained from a random sample of size n generated from fstar.

Usage

ISE_fstar(h, n)

Arguments

h

numerical vector of bandwidth values,

n

sample size (number of data points generated from fstar).

Details

The integrated squared error (ISE) is a measure of closeness of the Gaussian density estimate computed from a data set generated from fstar to the true density.

Value

The vector of values of the ISE function for the correponsing vector of h values.

References

Savchuk, O.Y. (2017). One-sided cross-validation for nonsmooth density functions, arXiv:1703.05157.

See Also

fstar, sample_fstar.

Examples

## Not run: 
dev.new()
harray=seq(0.05,1.5,len=1000)
ISEarray=ISE_fstar(harray,100)
h_ISE=round(harray[which.min(ISEarray)],digits=4)
dev.new()
plot(harray,ISEarray,lwd=3,'l',xlab="h",ylab="ISE",main="ISE(h)",cex.main=2,cex.lab=1.7,
cex.axis=1.7)
legend(0.35,ISEarray[5],legend=c("n=100",paste("h_ISE=",h_ISE)),cex=1.8,bty="n")

## End(Not run)