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Squared error bandwidth matrix selectors for normal mixture densities

ise.mixt.Rd

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.

Usage

Hamise.mixt(mus, Sigmas, props, samp, Hstart, deriv.order=0)
Hmise.mixt(mus, Sigmas, props, samp, Hstart, deriv.order=0)
Hamise.mixt.diag(mus, Sigmas, props, samp, Hstart, deriv.order=0)
Hmise.mixt.diag(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)
amise.mixt(H, mus, Sigmas, props, samp, h, sigmas, deriv.order=0)
ise.mixt(x, H, mus, Sigmas, props, h, sigmas, deriv.order=0, binned=FALSE, 
         bgridsize)  
mise.mixt(H, mus, Sigmas, props, samp, h, sigmas, deriv.order=0)

Arguments

mus

(stacked) matrix of mean vectors (>1-d), vector of means (1-d)

Sigmas,sigmas

(stacked) matrix of variance matrices (>1-d), vector of standard deviations (1-d)

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)

binned

flag for binned kernel estimation. Default is FALSE.

bgridsize

vector of binning grid sizes

Value

MISE- or AMISE-optimal bandwidth matrix. ISE, MISE or AMISE value.

Details

ISE is a random variable that depends on the data x. MISE and AMISE are non-random and don't depend on the data. For normal mixture densities, ISE, MISE and AMISE have exact formulas for all dimensions.

References

Chacon J.E., Duong, T. & Wand, M.P. (2011). Asymptotics for general multivariate kernel density derivative estimators. Statistica Sinica, 21, 807–840.

Examples

x <- rmvnorm.mixt(100)
Hamise.mixt(samp=nrow(x), mus=rep(0,2), Sigmas=var(x), props=1, deriv.order=1)
#>            [,1]       [,2]
#> [1,] 0.27764396 0.00883043
#> [2,] 0.00883043 0.27586662