ks (version 1.2.1)

Hpi, Hpi.diag: Plug-in bandwidth matrix selector for bivariate data

Description

Plug-in bandwidth matrix for bivariate data.

Usage

Hpi(x, nstage=2, pilot="samse", pre="sphere", Hstart)
Hpi.diag(x, nstage=2, pilot="amse", pre="scale", Hstart)

Arguments

x

matrix of data values

nstage

number of stages in the plug-in bandwidth selector (1 or 2)

pilot

"amse" = AMSE-optimal pilot bandwidths, "samse" = single SAMSE-optimal pilot bandwidth

pre

"scale" = pre-scaling, "sphere" = pre-sphering

Hstart

initial bandwidth matrix, used in numerical optimisation

Value

• Plug-in bandwidth matrix.

Details

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. Both of these pilot bandwidths require numerical optimisation.

For details on the pre-transformations in pre, see pre.sphere and pre.scale.

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

Wand, M.P. & Jones, M.C. (1994) Multivariate plugin bandwidth selection. Computational Statistics 9, 97-116. Duong, T. & Hazelton, M.L. (2003) Plug-in bandwidth matrices for bivariate kernel density estimation. Journal of Nonparametric Statistics 15, 17-30.

Examples

data(unicef)
Hpi(unicef, nstage=1, pilot="amse", pre="scale")
Hpi(unicef, nstage=2, pilot="samse", pre="sphere")
Hpi.diag(unicef, nstage=2, pilot="amse", pre="scale")