Hlscv, Hlscv.diag, hlscv {ks} | R Documentation |
LSCV bandwidth for 1- to 6-dimensional data
Hlscv(x, Hstart) Hlscv.diag(x, Hstart, binned=FALSE, bgridsize)
x |
vector or matrix of data values |
Hstart |
initial bandwidth matrix, used in numerical optimisation |
binned |
flag for binned kernel estimation |
bgridsize |
vector of binning grid sizes -
required only if binned=TRUE |
hlscv
is the univariate SCV
selector of Bowman (1984) and Rudemo (1982). Hlscv
is a
multivariate generalisation of this.
Use Hlscv
for full bandwidth matrices and Hlscv.diag
for diagonal bandwidth matrices.
For d = 2, 3, 4 and binned=TRUE
,
estimates are computed over a binning grid defined
by bgridsize
. Otherwise it's computed exactly.
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.
LSCV bandwidth.
Bowman, A. (1984) An alternative method of cross-validation for the smoothing of kernel density estimates. Biometrika. 71, 353-360.
Duong, T. & Hazelton, M.L. (2005) Cross-validation bandwidth matrices for multivariate kernel density estimation. Scandinavian Journal of Statistics. 32, 485-506.
Rudemo, M. (1982) Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics. 9, 65-78.
Sain, S.R, Baggerly, K.A & Scott, D.W. (1994) Cross-validation of multivariate densities. Journal of the American Statistical Association. 82, 1131-1146.
mus <- rbind(c(-1/2,0), c(1/2,0)) Sigmas <- rbind(diag(c(1/16, 1)), rbind(c(1/8, 1/16), c(1/16, 1/8))) props <- c(2/3, 1/3) x <- rmvnorm.mixt(1000, mus, Sigmas, props) Hlscv(x) Hlscv.diag(x, binned=TRUE)