LSCV bandwidth for 1- to 6-dimensional data

1 2 3 4 5 6 7 8 | ```
Hlscv(x, Hstart, binned=FALSE, bgridsize, amise=FALSE, deriv.order=0,
verbose=FALSE, optim.fun="nlm", trunc)
Hlscv.diag(x, Hstart, binned=FALSE, bgridsize, amise=FALSE, deriv.order=0,
verbose=FALSE, optim.fun="nlm", trunc)
hlscv(x, binned=TRUE, bgridsize, amise=FALSE, deriv.order=0)
Hucv(...)
Hucv.diag(...)
hucv(...)
``` |

`x` |
vector or matrix of data values |

`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 LSCV value. Default is FALSE. |

`deriv.order` |
derivative order |

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

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

`trunc` |
parameter to control truncation for numerical optimisation. Default is 4 for density.deriv>0, otherwise no truncation. For details see below. |

`...` |
parameters as above |

`hlscv`

is the univariate LSCV
selector of Bowman (1984) and Rudemo (1982). `Hlscv`

is a
multivariate generalisation of this. Use `Hlscv`

for unconstrained
bandwidth matrices and `Hlscv.diag`

for diagonal bandwidth matrices.
`Hucv`

, `Hucv.diag`

and `hucv`

are aliases with UCV
unbiased cross validation instead of LSCV.

Truncation of the parameter space is usually required for the LSCV selector,
for r > 0, to find a reasonable solution to the numerical optimisation.
If a candidate matrix `H`

is
such that `det(H)`

is not in `[1/trunc, trunc]*det(H0)`

or
`abs(LSCV(H)) > trunc*abs(LSCV0)`

then the `LSCV(H)`

is reset to `LSCV0`

where
`H0=Hns(x)`

and `LSCV0=LSCV(H0)`

.

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

,
see `Hpi`

.

LSCV bandwidth. If `amise=TRUE`

then the minimal LSCV value is returned too.

Bowman, A. (1984) An alternative method of cross-validation for the
smoothing of kernel density estimates. *Biometrika*. **71**,
353-360.

Rudemo, M. (1982) Empirical choice of histograms and kernel density
estimators. *Scandinavian Journal of Statistics*. **9**,
65-78.

1 2 3 4 |

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