ks (version 1.3.2)

Hmise.mixt, Hamise.mixt: MISE- and AMISE-optimal bandwidth matrix selectors for normal mixture densities

Description

For normal mixture densities, we have a closed form for the MISE and AMISE. So in these cases, we can numerically minimise these criteria to find MISE- and AMISE-optimal matrices.

Usage

Hmise.mixt(mus, Sigmas, props, samp, Hstart)
Hamise.mixt(mus, Sigmas, props, samp, Hstart)

Arguments

mus

(stacked) matrix of mean vectors

Sigmas

(stacked) matrix of variance matrices

props

vector of mixing proportions

samp

sample size

Hstart

initial bandwidth matrix, used in numerical optimisation

Value

• Full MISE- or AMISE-optimal bandwidth matrix. Please note that diagonal forms of these matrices are not available.

Details

For normal mixture densities, the MISE and AMISE have exact formulas. See Wand & Jones (1995).

If Hstart is not given then it defaults to k*var(x) where k = $\left[\frac{4}{n(d+2)}\right]^{2/(d+4)}$, n = sample size, d = dimension of data.

References

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

Examples

mus <- rbind(c(0,0,0), c(2,2,2))
Sigma <- matrix(c(1, 0.7, 0.7, 0.7, 1, 0.7, 0.7, 0.7, 1), nr=3, nc=3) 
Sigmas <- rbind(Sigma, Sigma)
props <- c(1/2, 1/2)
samp <- 1000
Hmise.mixt(mus, Sigmas, props, samp)
Hamise.mixt(mus, Sigmas, props, samp)