cencovariance  R Documentation 
This function estimates the centred covariance of a stationary RACS. Available estimators are the plugin moment centred covariance estimator, two 'balanced' estimators suggested by Picka (2000), and a third 'balanced' estimator inspired by one of Picka's paircorrelation estimators.
cencovariance( xi, obswin = NULL, setcov_boundarythresh = NULL, estimators = "all", drop = FALSE ) cencovariance.cvchat( cvchat, cpp1 = NULL, phat = NULL, setcov_boundarythresh = NULL, estimators = "all", drop = FALSE )
xi 
An observation of a RACS of interest as a full binary map (as an 
obswin 
If 
setcov_boundarythresh 
To avoid instabilities caused by dividing by very small quantities, if the set covariance of the observation window
is smaller than 
estimators 
A list of strings specifying estimators to use.
See details.

drop 
If TRUE and one estimator selected then the returned value will be a single 
cvchat 
The plugin moment estimate of covariance as an 
cpp1 
Picka's reduced window estimate of coverage probability as an 
phat 
The usual estimate of coverage probability,
which is the observed foreground area in 
The centred covariance of a stationary RACS is
κ(v) = C(v)  p^2.
The estimators available are (see (Section 3.4, Hingee, 2019) for more information):
plugin
the plugin moment centred
covariance estimator
mattfeldt
an estimator inspired by an
'intrinsically' balanced paircorrelation estimator from Picka (1997) that was
later studied in an isotropic situation by Mattfeldt and Stoyan
(Mattfeldt and Stoyan, 2000)
pickaint
Picka's 'intrinsically' balanced
centred covariance estimator (Picka, 2000).
pickaH
Picka's
'additively' balanced centred covariance estimator (Picka, 2000).
Currently computes centred covariance using racscovariance
.
If drop = TRUE
and only one estimator is requested then a
im
object containing the centred covariance estimate is returned. Otherwise a
named imlist
of im
objects containing the centred covariance
estimates for each requested estimator.
cencovariance
: Centred covariance estimates from a binary map.
cencovariance.cvchat
: Generates centred covariances estimates from
a plugin moment estimate of covariance, Picka's reduced window estimate of coverage probability,
and the plugin moment estimate of coverage probability.
If these estimates already exist, then cencovariance.cvchat
saves significant computation time over cencovariance
.
Kassel Liam Hingee
Hingee, K.L. (2019) Spatial Statistics of Random Closed Sets for Earth Observations. PhD: Perth, Western Australia: University of Western Australia. Submitted.
Mattfeldt, T. and Stoyan, D. (2000) Improved estimation of the pair correlation function of random sets. Journal of Microscopy, 200, 158173.
Picka, J.D. (1997) VarianceReducing Modifications for Estimators of Dependence in Random Sets. Ph.D.: Illinois, USA: The University of Chicago.
Picka, J.D. (2000) Variance reducing modifications for estimators of standardized moments of random sets. Advances in Applied Probability, 32, 682700.
xi < heather$coarse obswin < Frame(xi) cencovariance(xi, obswin, estimators = "all")
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