ise, mise, amise {ks}R Documentation

ISE, MISE and AMISE of kernel density estimates for normal and t mixture densities

Description

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.

Usage

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)

Arguments

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

Details

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.

Value

ISE, MISE or AMISE value.

Note

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.

References

Wand, M.P. & Jones, M.C. (1995) Kernel Smoothing. Chapman & Hall. London.

Examples

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))

[Package ks version 1.2.1 Index]