ISE_mixnorm {ICV}

The ISE function in the case when the underlying density is the specified mixture of normal distributions.

Description

Computing ISE(h) for given h in the case when the underlying density is the specified mixture of normal distributions and the Gaussian kernel is used to compute the ultimate density estimate.

Usage

ISE_mixnorm(h, x, w, mu, sdev)

Arguments

h

numerical vector of bandwidth values,

x

numerical vector of data,

w

vector of weighs (positive numbers between 0 and 1 that add up to one),

mu

vector of means,

sdev

vector of standard deviations.

Details

Computing ISE(h) in the case when the true density is the mixture of normal distributions defined by the vector of weights w, the vector of means \mu, and the vector of standard deviations \sigma. See expression (2.3) of Marron and Wand (1992). It is assumed that the normals are defined as parsimonious as possible. The normal distributions in the mixture should be ordered such that the means in \mu are arranged in a nondecreasing order. The Gaussian kernel is to be used for computing the ultimate density estimate.

Value

The vector of ISE values corresponding to the specifies values of h.

References

Marron, J.S., Wand, M.P. (1992). Exact Mean Integrated Squared Error. The Annals of Statistics, 20(2), 712-736.

See Also

mixnorm, h_isemixnorm, MISE_mixnorm.

Examples

## Not run: 
harg=seq(0.01,1,len=100)
w=c(3/4,1/4)
mu=c(0,3/2)
sdev=c(1,1/3)
# The vectors w, mu, and sdev define the skewed bimodal density of Marron and Wand (1992).
dat=mixnorm(300,w,mu,sdev)
h_ISE=round(h_isemixnorm(dat,w,mu,sdev),digits=4)
ISEarray=ISE_mixnorm(harg,dat,w,mu,sdev)
dev.new()
plot(harg,ISEarray,'l',lwd=3,xlab="h, n=300",ylab="ISE",cex.lab=1.7,cex.axis=1.7,main="")
title(main="ISE(h)",cex.main=1.7)
legend(0.2,0.08,legend=paste("h_ISE=",h_ISE),cex=2)

## End(Not run)