SCV bandwidth for 1- to 6-dimensional data.

```
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" = `pre.scale`

, "sphere" = `pre.sphere`

pilot

"amse" = AMSE pilot bandwidths "samse" = single SAMSE pilot bandwidth "unconstr" = single unconstrained pilot bandwidth "dscalar" = single pilot bandwidth for deriv.order>0 "dunconstr" = single unconstrained pilot bandwidth for deriv.order>0

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 `nlm`

or `optim`

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.

SCV bandwidth. If `amise=TRUE`

then the minimal scaled SCV value is returned too.

`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`

.

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.

```
# NOT RUN {
data(unicef)
Hscv(unicef)
hscv(unicef[,1])
# }
```

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