ks (version 1.8.4)

Hpi: Plug-in bandwidth selector

Description

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

Usage

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

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" = unconstrained pilot bandwidth, "dsamse" = single SAMSE pilot bandwidth for deriv.order>0, "dsc

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 is the univariate plug-in selector of Wand & Jones (1994), i.e. it is exactly the same as KernSmooth's dpik. Hpi is a multivariate generalisation of this. Use Hpi for full bandwidth matrices and Hpi.diag for diagonal bandwidth matrices.

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 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 k*var(x) where $k=\left[\frac{4}{n(d+2)}\right]^{2/(d+4)}$, n = sample size, d = dimension of data.

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 plugin bandwidth selection. Computational Statistics, 9, 97-116.

See Also

Hbcv, Hlscv, Hscv

Examples

data(unicef)
Hpi(unicef)
Hpi(unicef, pilot="unconstr")
Hpi.diag(unicef, binned=TRUE)
hpi(unicef[,1])