ks (version 1.4.2)

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)

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)