# cencovariance: Centred covariance estimation In lacunaritycovariance: Gliding Box Lacunarity and Other Metrics for 2D Random Closed Sets

 cencovariance R Documentation

## Centred covariance estimation

### Description

This function estimates the centred covariance of a stationary RACS. Available estimators are the plug-in moment centred covariance estimator, two 'balanced' estimators suggested by Picka (2000), and a third 'balanced' estimator inspired by one of Picka's pair-correlation estimators.

### Usage

```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
)
```

### Arguments

 `xi` An observation of a RACS of interest as a full binary map (as an `im` object) or as the foreground set (as an `owin` object). In the latter case the observation window, `obswin`, must be supplied. `obswin` If `xi` is an `owin` object then `obswin` is an `owin` object that specifies the observation window. `setcov_boundarythresh` To avoid instabilities caused by dividing by very small quantities, if the set covariance of the observation window is smaller than `setcov_boundarythresh`, then the covariance is given a value of NA. `estimators` A list of strings specifying estimators to use. See details. `estimators = "all"` will select all available estimators. `drop` If TRUE and one estimator selected then the returned value will be a single `im` object and not a list of `im` object. `cvchat` The plug-in moment estimate of covariance as an `im` object. Typically created with `plugincvc`. `cpp1` Picka's reduced window estimate of coverage probability as an `im` object - used in improved (balanced) covariance estimators. Can be generated using `cppicka`. `phat` The usual estimate of coverage probability, which is the observed foreground area in `xi` divided by the total area of the observation window. See `coverageprob` for more information.

### Details

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 plug-in moment centred covariance estimator

• `mattfeldt` an estimator inspired by an 'intrinsically' balanced pair-correlation 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`.

### Value

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.

### Functions

• `cencovariance`: Centred covariance estimates from a binary map.

• `cencovariance.cvchat`: Generates centred covariances estimates from a plug-in moment estimate of covariance, Picka's reduced window estimate of coverage probability, and the plug-in moment estimate of coverage probability. If these estimates already exist, then `cencovariance.cvchat` saves significant computation time over `cencovariance`.

### Author(s)

Kassel Liam Hingee

### References

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, 158-173.

Picka, J.D. (1997) Variance-Reducing 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, 682-700.

### Examples

```xi <- heather\$coarse
obswin <- Frame(xi)
cencovariance(xi, obswin, estimators = "all")

```

lacunaritycovariance documentation built on March 18, 2022, 5:20 p.m.