# lohboot

0th

Percentile

##### Bootstrap Confidence Bands for Summary Function

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

Keywords
spatial, nonparametric
##### 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 to be computed: one of the strings "pcf", "Kest", "Lest", "pcfinhom", "Kinhom" or "Linhom".
...
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.
##### 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 Lest localK pcfinhom localpcfinhom Kinhom localKinhom Linhom 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. An alternative to lohboot is varblock.

##### 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.

##### References

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

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

See varblock for an alternative bootstrap technique.

• lohboot
##### Examples
p <- lohboot(simdat, stoyan=0.5)
plot(p)
Documentation reproduced from package spatstat, version 1.34-1, License: GPL (>= 2)

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