Squared error bandwidth matrix selectors for normal mixture densities

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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

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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

Full 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

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x <- rmvnorm.mixt(100)
Hamise.mixt(samp=nrow(x), mus=rep(0,2), Sigmas=var(x), props=1, deriv.order=1)

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