ks (version 1.4.0)

Hscv: Smoothed cross-validation (SCV) bandwidth matrix selector for bivariate data

Description

SCV bandwidth matrix for 2- to 6-dimensional data.

Usage

Hscv(x, pre="sphere", Hstart, binned=FALSE)

Arguments

x

matrix of data values

pre

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

Hstart

initial bandwidth matrix, used in numerical optimisation

binned

if TRUE (default) used binned estimation otherwise use exact kernel density estimation

Value

• Full SCV bandwidth matrix. Please note that a diagonal version of this selector is not available.

Details

This SCV selector is a generalisation of the univariate SCV selector of Jones, Marron & Park (1991).

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

Jones, M.C., Marron, J.~S. & Park, B.U. (1991) A simple root n bandwidth selector. The Annals of Statistics 19, 1919--1932.

Duong, T. & Hazelton, M.L. (2005) Cross-validation bandwidth matrices for multivariate kernel density estimation. Scandinavian Journal of Statistics. 32, 485-506.

See Also

Hlscv, Hbcv

Examples

data(unicef)
Hscv(unicef)