Hamise.mixt, Hmise.mixt, amise.mixt, ise.mixt, mise.mixt {ks} | R Documentation |
The global errors ISE (Integrated Squared Error), MISE (Mean Integrated Squared Error) and the AMISE (Asymptotic Mean Integrated Squared Error) for 1- to 6-dimensional data.
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.
Hamise.mixt(mus, Sigmas, props, samp, Hstart, deriv.order=0) Hmise.mixt(mus, Sigmas, props, samp, Hstart, deriv.order=0) hamise.mixt(mus, sigmas, props, samp, hstart, deriv.order=0) hmise.mixt(mus, sigmas, props, samp, hstart, deriv.order=0) ise.mixt(x, H, mus, Sigmas, props, h, sigmas, deriv.order=0) mise.mixt(H, mus, Sigmas, props, samp, h, sigmas, deriv.order=0) amise.mixt(H, mus, Sigmas, props, samp, h, sigmas, deriv.order=0)
mus |
(stacked) matrix of mean vectors/vector of means |
sigmas, Sigmas |
vector of standard deviations/(stacked) matrix of variance matrices |
props |
vector of mixing proportions |
samp |
sample size |
hstart, Hstart |
initial bandwidth (matrix), used in numerical optimisation |
deriv.order |
derivative order |
x |
matrix of data values |
h, H |
bandwidth (matrix) |
For normal mixture densities, ISE, MISE and AMISE have exact formulas for all dimensions. See Chac'on, Duong & Wand (2008).
If Hstart
is not given then it defaults to
k*var(x)
where k =
4/(n*(d + 2r +
2))^(2/(d+ 2r+ 4)), n = sample size, d = dimension of data, r=
derivative order. The default for hstart
is the square root of
this expression.
– Full MISE- or AMISE-optimal bandwidth matrix. Diagonal forms of
these matrices are not available.
– ISE, MISE or AMISE value. ise
is not
yet available for deriv.order>0
.
ISE is a random variable that depends on the data
x
. MISE and AMISE are non-random and don't
depend on the data.
Chac'on J.E., Duong, T. & Wand, M.P. (2008) Asymptotics for general multivariate kernel density derivative estimators. In preparation.
## 1-d mus <- c(0, 2) sigmas <- c(1, sqrt(0.7)) props <- c(1/2, 1/2) samp <- 1000 h <- hmise.mixt(mus, sigmas, props, samp, deriv.order=0) x <- rnorm.mixt(n=samp, mus=mus, sigmas=sigmas, props=props) ise.mixt(x=x, h=h, mus=mus, sigmas=sigmas, props=props) mise.mixt(h=h, mus=mus, sigmas=sigmas, props=props, samp=samp) ## 2-d mus <- rbind(c(0,0), c(2,2)) Sigma <- matrix(c(1, 0.7, 0.7, 1), nr=2, nc=2) Sigmas <- rbind(Sigma, Sigma) props <- c(1/2, 1/2) samp <- 100 H <- Hamise.mixt(mus, Sigmas, props, samp, deriv.order=2) x <- rmvnorm.mixt(n=samp, mus=mus, Sigmas=Sigmas, props=props) amise.mixt(H=H, mus=mus, Sigmas=Sigmas, props=props, samp=samp, deriv.order=2)