pre.sphere, pre.scale {ks}R Documentation

Pre-sphering and pre-scaling

Description

Pre-sphered or pre-scaled version of data.

Usage

pre.sphere(x)
pre.scale(x)

Arguments

x matrix of data values

Details

For pre-scaling, the data values are pre-multiplied by S^(-1/2) and for pre-scaling, by S_D^(-1/2) where S is the sample variance and S_D is diag (S_1^2, S_2^2, ..., S_d^2) where S_i^2 is the i-th marginal sample variance.

If H* is the bandwidth matrix for the pre-transformed data and H is the bandwidth matrix for the original data, then S^(1/2) H* S^(1/2) or S_D^(1/2) H* S_D^(1/2) as appropriate.

Value

Pre-sphered or pre-scaled version of data. These pre-transformations are required for implementing the plug-in Hpi selectors and the smoothed cross validation Hscv selectors.

References

Wand, M.P. & Jones, M.C. (1994) Multivariate plugin bandwidth selection. Computational Statistics 9, 97-116.

Duong, T. & Hazelton, M.L. (2003) Plug-in bandwidth matrices for bivariate kernel density estimation. Journal of Nonparametric Statistics 15, 17-30.

Examples

x <- rmvnorm.mixt(1000, mus=c(0,0), Sigmas=rbind(c(1,0.2), c(0.2, 0.5))) 
x.sp <- pre.sphere(x)
x.sc <- pre.scale(x)
var(x.sp)
var(x.sc)

[Package ks version 1.4.0 Index]