ks (version 1.6.5)

Hlscv, Hlscv.diag, hlscv: Least-squares cross-validation (LSCV) bandwidth matrix selector for multivariate data

Description

LSCV bandwidth for 1- to 6-dimensional data

Usage

Hlscv(x, Hstart)
Hlscv.diag(x, Hstart, binned=FALSE, bgridsize)

Arguments

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

Value

• LSCV bandwidth.

Details

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

References

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.

See Also

Hbcv, Hscv

Examples

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)