ks: ise.mixt – R documentation

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ise.mixt

Squared error bandwidth matrix selectors for normal mixture densities

Description

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

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.

Value

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

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)

ks

Kernel Smoothing

v1.12.0

GPL-2 | GPL-3

Authors

Tarn Duong [aut, cre], Matt Wand [ctb], Jose Chacon [ctb], Artur Gramacki [ctb]

Initial release

2021-02-06