spatstat (version 1.52-1)

lohboot: Bootstrap Confidence Bands for Summary Function

Description

Computes a bootstrap confidence band for a summary function of a point process.

Usage

lohboot(X,
          fun=c("pcf", "Kest", "Lest", "pcfinhom", "Kinhom", "Linhom"),
          …, nsim=200, confidence=0.95, global=FALSE, type=7)

Arguments

X

A point pattern (object of class "ppp").

fun

Name of the summary function for which confidence intervals are desired: one of the strings "pcf", "Kest", "Lest", "pcfinhom", "Kinhom" or "Linhom". Alternatively, the function itself; it must be one of the functions listed here.

…

Arguments passed to the corresponding local version of the summary function (see Details).

nsim

Number of bootstrap simulations.

confidence

Confidence level, as a fraction between 0 and 1.

global

Logical. If FALSE (the default), pointwise confidence intervals are constructed. If TRUE, a global (simultaneous) confidence band is constructed.

type

Integer. Argument passed to quantile controlling the way the quantiles are calculated.

Value

A function value table (object of class "fv") containing columns giving the estimate of the summary function, the upper and lower limits of the bootstrap confidence interval, and the theoretical value of the summary function for a Poisson process.

Details

This algorithm computes confidence bands for the true value of the summary function fun using the bootstrap method of Loh (2008).

If fun="pcf", for example, the algorithm computes a pointwise (100 * confidence)% confidence interval for the true value of the pair correlation function for the point process, normally estimated by pcf. It starts by computing the array of local pair correlation functions, localpcf, of the data pattern X. This array consists of the contributions to the estimate of the pair correlation function from each data point. Then these contributions are resampled nsim times with replacement; from each resampled dataset the total contribution is computed, yielding nsim random pair correlation functions. The pointwise alpha/2 and 1 - alpha/2 quantiles of these functions are computed, where alpha = 1 - confidence. The average of the local functions is also computed as an estimate of the pair correlation function.

To control the estimation algorithm, use the arguments …, which are passed to the local version of the summary function, as shown below:

fun	local version
pcf	localpcf
Kest	localK
Lest	localK
pcfinhom	localpcfinhom
Kinhom	localKinhom

For fun="Lest", the calculations are first performed as if fun="Kest", and then the square-root transformation is applied to obtain the \(L\)-function.

Note that the confidence bands computed by lohboot(fun="pcf") may not contain the estimate of the pair correlation function computed by pcf, because of differences between the algorithm parameters (such as the choice of edge correction) in localpcf and pcf. If you are using lohboot, the appropriate point estimate of the pair correlation itself is the pointwise mean of the local estimates, which is provided in the result of lohboot and is shown in the default plot.

If the confidence bands seem unbelievably narrow, this may occur because the point pattern has a hard core (the true pair correlation function is zero for certain values of distance) or because of an optical illusion when the function is steeply sloping (remember the width of the confidence bands should be measured vertically).

An alternative to lohboot is varblock.

References

Loh, J.M. (2008) A valid and fast spatial bootstrap for correlation functions. The Astrophysical Journal, 681, 726--734.

See Also

Summary functions Kest, pcf, Kinhom, pcfinhom, localK, localpcf, localKinhom, localpcfinhom.

See varblock for an alternative bootstrap technique.

Examples

# NOT RUN {
  p <- lohboot(simdat, stoyan=0.5)
  plot(p)
# }