Hbcv, Hbcv.diag: 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

Value

BCV bandwidth matrix.

Details

Use Hbcv for full bandwidth matrices and Hbcv.diag for diagonal bandwidth matrices.

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

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.

Examples

Run this code

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

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