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Hpi

Plug-in bandwidth selector

Description

Plug-in bandwidth for for 1- to 6-dimensional data.

Usage

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

Arguments

`x`	vector or matrix of data values
`nstage`	number of stages in the plug-in bandwidth selector (1 or 2)
`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
`pre`	"scale" = `pre.scale`, "sphere" = `pre.sphere`
`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 PI value
`deriv.order`	derivative order
`verbose`	flag to print out progress information. Default is FALSE.
`optim.fun`	optimiser function: one of `nlm` or `optim`

Details

hpi(,deriv.order=0) is the univariate plug-in selector of Wand & Jones (1994), i.e. it is exactly the same as KernSmooth's dpik. For deriv.order>0, the formula is taken from Wand & Jones (1995). Hpi is a multivariate generalisation of this. Use Hpi for unconstrained bandwidth matrices and Hpi.diag for diagonal bandwidth matrices.

The default pilot is "samse" for d=2,r=0, and "dscalar" otherwise. For AMSE pilot bandwidths, see Wand & Jones (1994). For SAMSE pilot bandwidths, see Duong & Hazelton (2003). The latter is a modification of the former, in order to remove any possible problems with non-positive definiteness. Unconstrained and higher order derivative pilot bandwidths are from Chacon & Duong (2010).

For d=1, 2, 3, 4 and binned=TRUE, estimates are computed over a binning grid defined by bgridsize. Otherwise it's computed exactly. If Hstart is not given then it defaults to Hns(x).

For ks >= 1.11.1, the default optimisation function is optim.fun="optim". To reinstate the previous functionality, use optim.fun="nlm".

Value

Plug-in bandwidth. If amise=TRUE then the minimal scaled PI value is returned too.

References

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

Duong, T. & Hazelton, M.L. (2003) Plug-in bandwidth matrices for bivariate kernel density estimation. Journal of Nonparametric Statistics, 15, 17-30.

Sheather, S.J. & Jones, M.C. (1991) A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society Series B, 53, 683-690.

Wand, M.P. & Jones, M.C. (1994) Multivariate plug-in bandwidth selection. Computational Statistics, 9, 97-116.

Examples

data(unicef)
Hpi(unicef, pilot="dscalar")
hpi(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

Hpi