ks (version 1.8.4)

Hscv: Smoothed cross-validation (SCV) bandwidth selector

Description

SCV bandwidth for 1- to 6-dimensional data.

Usage

Hscv(x, nstage=2, pre="sphere", pilot="samse", Hstart, binned=FALSE, 
     bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, 
     optim.fun="nlm")
Hscv.diag(x, nstage=2, pre="scale", pilot="samse", Hstart, binned=FALSE, 
     bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, 
     optim.fun="nlm")
hscv(x, nstage=2, binned=TRUE, bgridsize, plot=FALSE)

Arguments

x

vector or matrix of data values

pre

"scale" = pre.scale, "sphere" = pre.sphere

pilot

"amse" = AMSE pilot bandwidths, "samse" = single SAMSE pilot bandwidth, "unconstr" = unconstrained pilot bandwidth matrix, "dsamse" = single SAMSE pilot bandwidth for deriv.order>0,

Hstart

initial bandwidth matrix, used in numerical optimisation

binned

flag for binned kernel estimation. Default is FALSE.

bgridsize

vector of binning grid sizes

amise

flag to return the minimal scaled SCV value. Default is FALSE.

deriv.order

derivative order

verbose

flag to print out progress information. Default is FALSE.

optim.fun

optimiser function: one of nlm or optim.

nstage

number of stages in the SCV bandwidth selector (1 or 2)

plot

flag to display plot of SCV(h) vs h (1-d only). Default is FALSE.

Value

• SCV bandwidth. If amise=TRUE then the minimal scaled SCV value is returned too.

Details

hsv is the univariate SCV selector of Jones, Marron & Park (1991). Hscv is a multivariate generalisation of this, see Duong & Hazelton (2005). Use Hscv for full bandwidth matrices and Hscv.diag for diagonal bandwidth matrices. For AMSE pilot bandwidths, see Wand & Jones (1994). For SAMSE pilot bandwidths, see Duong & Hazelton (2003). The latter is a modification of the former, in order to remove any possible problems with non-positive definiteness. Unconstrained pilot bandwidths are from Chacon & Duong (2011).

For d = 1, the selector hscv is not always stable for large sample sizes with binning. Examine the plot from hscv(, plot=TRUE) to determine the appropriate smoothness of the SCV function. Any non-smoothness is due to the discretised nature of binned estimation. For details about the advanced options for binned, Hstart, see Hpi.

References

Chacon, J.E. & Duong, T. (2011) Unconstrained pilot selectors for smoothed cross validation. Australian & New Zealand Journal of Statistics. Accepted. Duong, T. & Hazelton, M.L. (2003) Plug-in bandwidth matrices for bivariate kernel density estimation. Journal of Nonparametric Statistics. 15, 17-30. Duong, T. & Hazelton, M.L. (2005) Cross-validation bandwidth matrices for multivariate kernel density estimation. Scandinavian Journal of Statistics. 32, 485-506.

Wand, M.P. & Jones, M.C. (1994) Multivariate plugin bandwidth selection. Computational Statistics, 9, 97-116. Jones, M.C., Marron, J.S. & Park, B.U. (1991) A simple root n bandwidth selector. Annals of Statistics 19, 1919-1932.

See Also

Hbcv, Hlscv, Hpi

Examples

data(unicef)
Hscv(unicef)
Hscv.diag(unicef, binned=TRUE)
hscv(unicef[,1])