Hmise.mixt, Hamise.mixt {ks}R Documentation

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

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 = 4/(n*(d + 2))^(2/(d+ 4)), n = sample size, d = dimension of data.

Value

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

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)


[Package ks version 1.3.2 Index]