normalise function

Transform the noise to be closer to the Gaussian distribution

This function pre-processes the given data in order to obtain a noise structure that is closer to satisfying the Gaussianity assumption. See details for more information and for the relevant literature reference.

normalise(x, sc = 3)

Arguments

• x: A numeric vector containing the data.
• sc: A positive integer number with default value equal to 3. It is used to define the way we pre-average the given data sequence.

Returns

The ``normalised'' vector $\tilde{x}$ of length $Q$, as explained in Details.

Details

For a given natural number sc and data x of length $T$, let us denote by $Q = \lceil T/sc \rceil$. Then, normalise calculates

for $q=1, 2, ..., Q-1$, while

More details can be found in the preprint ``Detecting multiple generalized change-points by isolating single ones'', Anastasiou and Fryzlewicz (2018).

Examples

t5 <- rt(n = 10000, df = 5)
n5 <- normalise(t5, sc = 3)

See Also

ht_ID_pcm and ht_ID_cplm, which are functions that employ normalise.

Author(s)

Andreas Anastasiou, a.anastasiou@lse.ac.uk