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

BCV bandwidth matrix for bivariate data.

Usage

Hbcv(x, whichbcv=1, Hstart, binned=FALSE, amise=FALSE, verbose=FALSE)
Hbcv.diag(x, whichbcv=1, Hstart, binned=FALSE, amise=FALSE, verbose=FALSE)

Arguments

x

matrix of data values

whichbcv

1 = BCV1, 2 = BCV2. See details below.

Hstart

initial bandwidth matrix, used in numerical optimisation

binned

flag for binned kernel estimation. Default is FALSE.

amise

flag to return the minimal BCV value. Default is FALSE.

verbose

flag to print out progress information. Default is FALSE.

Value

BCV bandwidth matrix. If amise=TRUE then the minimal BCV value is returned too.

Details

Use Hbcv for unconstrained bandwidth matrices and Hbcv.diag for diagonal bandwidth matrices. These selectors are only available for bivariate data. Two types of BCV criteria are considered here. They are known as BCV1 and BCV2, from Sain, Baggerly & Scott (1994) and only differ slightly. These BCV surfaces can have multiple minima and so it can be quite difficult to locate the most appropriate minimum. Some times, there can be no local minimum at all so there may be no finite BCV selector.

For details about the advanced options for binned, Hstart, see Hpi.

See also

Hlscv, Hpi, Hscv

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.

Examples

data(unicef)
Hbcv(unicef)
#>           [,1]      [,2]
#> [1,] 1207.8536 150.36740
#> [2,]  150.3674  26.20683
Hbcv.diag(unicef)
#>          [,1]     [,2]
#> [1,] 1072.781 0.000000
#> [2,]    0.000 9.298473