Hbcv, Hbcv.diag {ks}R Documentation

Biased cross-validation (BCV) bandwidth matrix selector for bivariate data

Description

BCV bandwidth matrix for bivariate data.

Usage

Hbcv(x, whichbcv=1, Hstart)
Hbcv.diag(x, whichbcv=1, Hstart)

Arguments

x matrix of data values
whichbcv 1 = BCV1, 2 = BCV2. See details below
Hstart initial bandwidth matrix, used in numerical optimisation

Details

Use Hbcv for full bandwidth matrices and Hbcv.diag for diagonal bandwidth matrices. These selectors are only available for bivariate data.

There are two types of BCV criteria considered here. They are known as BCV1 and BCV2, from Sain, Baggerly & Scott (1994) and they only differ slightly. These BCV surfaces can have multiple minima and so it can be quite difficult to locate the most appropriate minimum.

If Hstart is not given then it defaults to k*var(x) where k = 4/(n*(d + 2))^(2/(d+ 4)), n = sample size, d = dimension of data.

Value

BCV bandwidth matrix.

Note

It can be difficult to find an appropriate (local) minimum of the BCV criterion. Some times, there can be no local minimum at all so there may be no finite BCV selector.

References

Sain, S.R, Baggerly, K.A. & Scott, D.W. (1994) Cross-validation of multivariate densities. Journal of the American Statistical Association. 82, 1131-1146.

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, Hscv

Examples

data(unicef)
Hbcv(unicef)
Hbcv.diag(unicef)

[Package ks version 1.6.2 Index]