ise, mise, amise {ks}R Documentation

ISE, MISE and AMISE of kernel density estimates for normal mixture densities

Description

The global errors ISE (Integrated Squared Error), MISE (Mean Integrated Squared Error) of kernel density estimates for normal densities, for 2- to 6-dimensional data, and and AMISE (Asymptotic Mean Integrated Squared Error) fpr 2-dimensional data.

Usage

ise.mixt(x, H, mus, Sigmas, props)  
mise.mixt(H, mus, Sigmas, props, samp)
amise.mixt(H, mus, Sigmas, props, samp)

Arguments

x matrix of data values
H bandwidth matrix
mus (stacked) matrix of mean vectors
Sigmas (stacked) matrix of variance matrices
props vector of mixing proportions
samp sample size

Details

For normal mixture densities, ISE and MISE have exact formulas for all dimensions, and AMISE has an exact form for 2 dimensions. See Wand & Jones (1995).

Value

ISE, MISE or AMISE value.

Note

Remember that ISE is a random variable that depends on the data x; and that MISE and AMISE are non-random and don't depend on the data.

References

Wand, M.P. & Jones, M.C. (1995) Kernel Smoothing. Chapman & Hall. London.

Examples

samp <- 50
d <- 3
mus <- rbind(rep(0,d), rep(1,d))
Sigmas <- 0.25*rbind(diag(d), diag(d))
props <- c(2/3, 1/3)
x <- rmvnorm.mixt(samp, mus, Sigmas, props)
H <- Hpi(x)
ise.mixt(x, H, mus, Sigmas, props)
mise.mixt(H, mus, Sigmas, props, samp)

[Package ks version 1.3.1 Index]