Hpi: Plug-in bandwidth selector

In ks: Kernel Smoothing

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 \geq 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.

See Also

Hbcv, Hlscv, Hscv

Examples

data(unicef)
Hpi(unicef, pilot="dscalar")
hpi(unicef[,1])

ks documentation built on Sept. 30, 2024, 9:15 a.m.