# Pre-sphering and pre-scaling

### Description

Pre-sphered or pre-scaled version of data.

### Usage

1 2 | ```
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. |

### 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.

### 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.

### Examples

1 2 | ```
data(unicef)
unicef.sp <- pre.sphere(as.matrix(unicef))
``` |

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