est_signal {IDetect} | R Documentation |
Estimate the signal
Description
This function estimates the signal in a given data sequence x
with change-points
at cpt
. The type of the signal depends on whether the change-points represent changes
in a piecewise-constant or continuous, piecewise-linear signal. For more information see
Details below.
Usage
est_signal(x, cpt, type = c("mean", "slope"))
Arguments
x |
A numeric vector containing the given data. |
cpt |
A positive integer vector with the locations of the change-points.
If missing, the |
type |
A character string, which defines the type of the detected change-points.
If |
Details
The data points provided in x
are assumed to follow
where is the total length of the data sequence,
are the observed
data,
is a one-dimensional, deterministic signal with abrupt structural
changes at certain points, and
is white noise. We denote by
the elements in
cpt
and by and
. Depending on the value that has been passed to
type
, the returned
value is calculated as follows.
-
For
type = ``mean''
, in each segment,
for
is approximated by the mean of
calculated over
.
-
For
type = ``slope''
,is approximated by the linear spline fit with knots at
minimising the
distance between the fit and the data.
Value
A numeric vector with the estimated signal.
Author(s)
Andreas Anastasiou, a.anastasiou@lse.ac.uk
Examples
single.cpt.pcm <- c(rep(4,1000),rep(0,1000))
single.cpt.pcm.noise <- single.cpt.pcm + rnorm(2000)
cpt.single.pcm <- ID_pcm(single.cpt.pcm.noise)
fit.cpt.single.pcm <- est_signal(single.cpt.pcm.noise, cpt.single.pcm$cpt, type = "mean")
three.cpt.pcm <- c(rep(4,500),rep(0,500),rep(-4,500),rep(1,500))
three.cpt.pcm.noise <- three.cpt.pcm + rnorm(2000)
cpt.three.pcm <- ID_pcm(three.cpt.pcm.noise)
fit.cpt.three.pcm <- est_signal(three.cpt.pcm.noise, cpt.three.pcm$pcm, type = "mean")
single.cpt.plm <- c(seq(0,999,1),seq(998.5,499,-0.5))
single.cpt.plm.noise <- single.cpt.plm + rnorm(2000)
cpt.single.plm <- ID_cplm(single.cpt.plm.noise)
fit.cpt.single.plm <- est_signal(single.cpt.plm.noise, cpt.single.plm$cpt, type = "slope")