ks (version 1.3.2)

ise, mise, amise: 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

Value

• ISE, MISE or AMISE value.

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).

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)