bw.ppl

Likelihood Cross Validation Bandwidth Selection for Kernel Density

Uses likelihood cross-validation to select a smoothing bandwidth for the kernel estimation of point process intensity.

Usage

bw.ppl(X, ..., srange=NULL, ns=32)

Details

This function selects an appropriate bandwidth sigma for the kernel estimator of point process intensity computed by density.ppp.

The bandwidth $\sigma$ is chosen to maximise the point process likelihood cross-validation criterion $$\mbox{LCV}(\sigma) = \sum_i \log\hat\lambda_{-i}(x_i) - \int_W \hat\lambda(u) \, {\rm d}u$$ where the sum is taken over all the data points $x_i$, where $\hat\lambda_{-i}(x_i)$ is the leave-one-out kernel-smoothing estimate of the intensity at $x_i$ with smoothing bandwidth $\sigma$, and $\hat\lambda(u)$ is the kernel-smoothing estimate of the intensity at a spatial location $u$ with smoothing bandwidth $\sigma$. See Loader(1999, Section 5.3).

The value of $\mbox{LCV}(\sigma)$ is computed directly, using density.ppp, for ns different values of $\sigma$ between srange[1] and srange[2].

The result is a numerical value giving the selected bandwidth. The result also belongs to the class "bw.optim" which can be plotted to show the (rescaled) mean-square error as a function of sigma.

References

Loader, C. (1999) Local Regression and Likelihood. Springer, New York.

See Also

density.ppp, bw.diggle, bw.scott

Aliases

• bw.ppl

Examples

b <- bw.ppl(redwood)
    plot(b, main="Likelihood cross validation for redwoods")
    plot(density(redwood, b))
  <testonly>b <- bw.ppl(redwood, srange=c(0.03, 0.07), ns=2)</testonly>