Kernel functional estimate for 1- to 6-dimensional data.

1 2 3 4 5 6 7 | ```
kfe(x, G, deriv.order, inc=1, binned=FALSE, bin.par, bgridsize, deriv.vec=TRUE,
add.index=TRUE, verbose=FALSE)
Hpi.kfe(x, nstage=2, pilot, pre="sphere", Hstart, binned=FALSE,
bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="nlm")
Hpi.diag.kfe(x, nstage=2, pilot, pre="scale", Hstart, binned=FALSE,
bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="nlm")
hpi.kfe(x, nstage=2, binned=FALSE, bgridsize, amise=FALSE, deriv.order=0)
``` |

`x` |
vector/matrix of data values |

`nstage` |
number of stages in the plug-in bandwidth selector (1 or 2) |

`pilot` |
"dscalar" = single pilot bandwidth (default) |

`pre` |
"scale" = |

`Hstart` |
initial bandwidth matrix, used in numerical optimisation |

`binned` |
flag for binned estimation. Default is FALSE. |

`bgridsize` |
vector of binning grid sizes |

`amise` |
flag to return the minimal scaled PI value |

`deriv.order` |
derivative order |

`verbose` |
flag to print out progress information. Default is FALSE. |

`optim.fun` |
optimiser function: one of |

`G` |
pilot bandwidth matrix |

`inc` |
0=exclude diagonal, 1=include diagonal terms in kfe calculation |

`bin.par` |
binning parameters - output from |

`deriv.vec` |
flag to compute duplicated partial derivatives in the vectorised form. Default is FALSE. |

`add.index` |
flag to ouput derivative indices matrix. Default is true. |

`Hpi.kfe`

is the optimal plug-in bandwidth for *r*-th order kernel functional estimator
based on the unconstrained pilot selectors of Chacon & Duong (2010).
`hpi.kfe`

is the 1-d equivalent, using the formulas from
Wand & Jones (1995, p.70).

`kfe`

does not usually need to be called explicitly by the user.

Plug-in bandwidth matrix for *r*-th order kernel functional estimator.

Chacon, J.E. & Duong, T. (2010) Multivariate plug-in bandwidth
selection with unconstrained pilot matrices. *Test*. **19**,
375-398.

Wand, M.P. & Jones, M.C. (1995) *Kernel Smoothing*. Chapman &
Hall/CRC, London.

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