ks (version 1.9.5)

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

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

Value

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

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 full 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).

References

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

Chacon, J.E. & Duong, T. (2015) Efficient recursive algorithms for functionals based on higher order derivatives of the multivariate Gaussian density. Statistics & Computing. 25, 959--974. 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 plugin bandwidth selection. Computational Statistics. 9, 97-116.

See Also

Hbcv, Hlscv, Hscv

Examples

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