normalise: Transform the noise to be closer to the Gaussian distribution

In IDetect: Isolate-Detect Method for Multiple Change-Point Detection

Transform the noise to be closer to the Gaussian distribution

Description

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.

Usage

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.

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

\tilde{x}_q = 1/sc\sum_{t=(q-1) * sc + 1}^{q * sc}x_t,

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

\tilde{x}_Q = (T - (Q-1) * sc)^{-1}\sum_{t = (Q-1) * sc + 1}^{T}x_t.

More details can be found in the preprint “Detecting multiple generalized change-points by isolating single ones”, Anastasiou and Fryzlewicz (2017).

Value

The “normalised” vector \tilde{x} of length Q, as explained in Details.

Author(s)

Andreas Anastasiou, [e-mail]

See Also

ht_ID_pcm, ht_ID_plm, and ID, which are functions that employ normalise.

Examples

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

IDetect documentation built on May 7, 2026, 5:09 p.m.