ise, mise, amise {ks} | R Documentation |
The global errors ISE (Integrated Squared Error), MISE (Mean Integrated Squared Error) and AMISE (Asymptotic Mean Integrated Squared Error) of kernel density estimates for normal and t mixture densities.
ise.mixt(x, H, mus, Sigmas, props, lower, upper, gridsize=c(250,250), stepsize) iset.mixt(x, H, mus, Sigmas, dfs, props, lower, upper, gridsize=c(250,250), stepsize) mise.mixt(H, mus, Sigmas, props, samp) amise.mixt(H, mus, Sigmas, props, samp)
x |
matrix of data values |
H |
bandwidth matrix |
mus |
(stacked) matrix of mean vectors |
Sigmas |
(stacked) matrix of variance matrices |
dfs |
vector of degrees of freedom |
props |
vector of mixing proportions |
samp |
sample size |
lower, upper |
vectors of lower, upper bounds for numerical integration |
gridsize |
vector of number of points in each dimension |
stepsize |
vector of step sizes in each dimension |
For normal mixture densities, the ISE, MISE and AMISE all
have exact formulas. See Wand & Jones (1995). For the t mixture
densities, we resort to using numerical integration, using a simple
Riemann sum. A grid is set up and the function values are computed
and then multiplied by the area of the grid element to give an
approximation of the volume under the curve. The resolution of the
grid is given either by gridsize
or stepsize
.
ISE, MISE or AMISE value.
Remember that ISE is a random variable that depends on the data
x
; and that 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.
samp <- 100 mus <- rbind(c(-3/2,0), c(3/2,0)) Sigmas <- rbind(diag(c(1/16, 1)), rbind(c(1/16, 1/18), c(1/18, 1/16))) props <- c(2/3, 1/3) x <- rmvnorm.mixt(samp, mus, Sigmas, props) H <- Hpi(x) ise.mixt(x, H, mus, Sigmas, props, stepsize=0.01) mise.mixt(H, mus, Sigmas, props, samp) amise.mixt(H, mus, Sigmas, props, samp) dfs <- c(7,5) x <- rmvt.mixt(samp, mus, Sigmas, dfs, props) H <- Hpi(x) iset.mixt(x, H, mus, Sigmas, dfs, props, lower=c(-5,-5), upper=c(5,5))