Hbcv, Hbcv.diag {ks} | R Documentation |
BCV bandwidth matrix for bivariate data.
Hbcv(x, whichbcv=1, Hstart) Hbcv.diag(x, whichbcv=1, Hstart)
x |
matrix of data values |
whichbcv |
1 = BCV1, 2 = BCV2. See details below |
Hstart |
initial bandwidth matrix, used in numerical optimisation |
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.
BCV bandwidth matrix.
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.
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.
data(unicef) Hbcv(unicef) Hbcv.diag(unicef)