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Hscv

Smoothed cross-validation (SCV) bandwidth selector

Description

SCV bandwidth for 1- to 6-dimensional data.

Usage

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

Arguments

`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
`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.

Details

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, optim.fun, see Hpi.

Value

SCV bandwidth. If amise=TRUE then the minimal scaled SCV value is returned too.

References

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.

Examples

data(unicef)
Hscv(unicef)
hscv(unicef[,1])

ks

Kernel Smoothing

v1.12.0

GPL-2 | GPL-3

Authors

Tarn Duong [aut, cre], Matt Wand [ctb], Jose Chacon [ctb], Artur Gramacki [ctb]

Initial release

2021-02-06