SCV bandwidth for 1- to 6-dimensional data.

1 2 3 4 5 | ```
Hscv(x, nstage=2, pre="sphere", pilot, Hstart, binned=FALSE,
bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="nlm")
Hscv.diag(x, nstage=2, pre="scale", pilot, Hstart, binned=FALSE,
bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="nlm")
hscv(x, nstage=2, binned=TRUE, bgridsize, plot=FALSE)
``` |

`x` |
vector or matrix of data values |

`pre` |
"scale" = |

`pilot` |
"amse" = AMSE pilot bandwidths |

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

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

`bgridsize` |
vector of binning grid sizes |

`amise` |
flag to return the minimal scaled SCV value. Default is FALSE. |

`deriv.order` |
derivative order |

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

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

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

`plot` |
flag to display plot of SCV(h) vs h (1-d only). Default is FALSE. |

`hscv`

is the univariate SCV
selector of Jones, Marron & Park (1991). `Hscv`

is a
multivariate generalisation of this, see Duong & Hazelton (2005).
Use `Hscv`

for unconstrained bandwidth matrices and `Hscv.diag`

for diagonal bandwidth matrices.

The default pilot is `"samse"`

for d=2, r=0, and
`"dscalar"`

otherwise. For SAMSE pilot bandwidths, see Duong &
Hazelton (2005). Unconstrained and higher order derivative pilot
bandwidths are from Chacon & Duong (2011).

For d=1, the selector `hscv`

is not always stable for large
sample sizes with binning.
Examine the plot from `hscv(, plot=TRUE)`

to
determine the appropriate smoothness of the SCV function. Any
non-smoothness is due to the discretised nature of binned estimation.

For details about the advanced options for `binned, Hstart`

,
see `Hpi`

.

SCV bandwidth. If `amise=TRUE`

then the minimal scaled SCV value is returned too.

Chacon, J.E. & Duong, T. (2011) Unconstrained pilot selectors for smoothed cross
validation. *Australian & New Zealand Journal of Statistics*. **53**, 331-351.

Duong, T. & Hazelton, M.L. (2005) Cross-validation bandwidth
matrices for multivariate kernel density estimation. *Scandinavian Journal
of Statistics*. **32**, 485-506.

Jones, M.C., Marron, J.S. & Park, B.U. (1991) A simple root n
bandwidth selector. *Annals of Statistics*. **19**, 1919-1932.

1 2 3 |

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