Exercise

# Bandwidth selection

We can get a more principled measure of the violent crime ratio using
a spatial segregation model. The `spatialkernel`

package implements the
theory of spatial segregation.

The first step is to compute the optimal bandwidth for kernel smoothing under the segregation model. A small bandwidth would result in a density that is mostly zero, with spikes at the event locations. A large bandwidth would flatten out any structure in the events, resulting in a large "blob" across the whole window. Somewhere between these extremes is a bandwidth that best represents an underlying density for the process.

`spseg()`

will scan over a range of bandwidths
and compute a test statistic using a cross-validation method. The bandwidth
that maximizes this test statistic is the one to use. The returned value from `spseg()`

in this case is a list, with
`h`

and `cv`

elements giving the values of the statistic over the input `h`

values. The `spatialkernel`

package supplies
a `plotcv`

function to show how the test value varies.
The `hcv`

element has the value of the best bandwidth.

Instructions

**100 XP**

`spatstat`

is loaded and the `preston_crime`

object is read in.

- Set
`h`

, the bandwidth values to try, then call`spseg()`

.- You need to provide the start value,
`500`

, then end value,`1000`

, and the step size,`50`

. - Assign the result to
`bw_choice`

.

- You need to provide the start value,
- Plot the test statistic vs. the bandwidth.
- Call
`plotcv()`

on`bw_choice`

. - Highlight the best bandwidth by adding a vertical line where the test statistic is maximized.

- Call