Hamise.mixt, Hmise.mixt {ks} | R Documentation |
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.
Hmise.mixt(mus, Sigmas, props, samp, Hstart) Hamise.mixt(mus, Sigmas, props, samp, Hstart)
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 |
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.
Full MISE- or AMISE-optimal bandwidth matrix. Please note that diagonal forms of these matrices are not available.
Wand, M.P. & Jones, M.C. (1995) Kernel Smoothing. Chapman & Hall. London.
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)