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.

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)
``` |

`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 |

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.

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

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

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

Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.

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