Hamise.mixt, Hmise.mixt, amise.mixt, ise.mixt, mise.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.
The global errors ISE (Integrated Squared Error), MISE (Mean Integrated Squared Error) of kernel density estimates for normal densities, for 2- to 6-dimensional data, and AMISE (Asymptotic Mean Integrated Squared Error) for 2-dimensional data.
Hmise.mixt(mus, Sigmas, props, samp, Hstart) Hamise.mixt(mus, Sigmas, props, samp, Hstart) ise.mixt(x, H, mus, Sigmas, props) mise.mixt(H, mus, Sigmas, props, samp) amise.mixt(H, mus, Sigmas, props, samp)
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 |
x |
matrix of data values |
H |
bandwidth matrix |
For normal mixture densities, ISE and MISE have exact formulas for all dimensions, and AMISE has an exact form for 2 dimensions. 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. Diagonal forms of
these matrices are not available.
– ISE, MISE or AMISE value.
ISE is a random variable that depends on the data
x
. MISE and AMISE are non-random and don't
depend on the data.
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 x <- rmvnorm.mixt(n=samp, mus=mus, Sigmas=Sigmas, props=props) H1 <- Hmise.mixt(mus, Sigmas, props, samp) H2 <- Hamise.mixt(mus, Sigmas, props, samp) ise.mixt(x, H2, mus, Sigmas, props) mise.mixt(H2, mus, Sigmas, props, samp)