ks (version 1.4.4)

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

Description

Normal mixture densities have closed form expressions 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)