spatstat (version 1.31-3)

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", "pcfinhom", "Kinhom"),
          ..., nsim=200, confidence=0.95, global=FALSE, type=7)

Arguments

X

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

fun

Name of the summary function to be computed: one of the strings "pcf", "Kest", "pcfinhom" or "Kinhom".

...

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 statistic 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 pcf for the point process. It starts by computing the array of local pair correlation functions, localpcf, of the data pattern X. This array consists of the contributions to pcf 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.

To control the smoothing and estimation algorithm, use the arguments ..., which are passed to the local version of the summary function, as shown below: ll{ fun local version pcf localpcf Kest localK pcfinhom localpcfinhom Kinhom localKinhom }

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

p <- lohboot(simdat, stoyan=0.5)
  plot(p)