# ise.mixt: Squared error bandwidth matrix selectors for normal mixture... In ks: Kernel Smoothing

## 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

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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

Unconstrained 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

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

ks documentation built on Jan. 20, 2018, 9:16 a.m.