Pre-sphering and pre-scaling

Pre-sphered or pre-scaled version of data.

Usage

pre.sphere(x, mean.centred=FALSE)
pre.scale(x, mean.centred=FALSE)

Arguments

x

matrix of data values

mean.centred

flag to centre the data values to have zero mean. Default is FALSE.

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.

Details

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

Examples

data(unicef)
unicef.sp <- pre.sphere(as.matrix(unicef))