# bw.relrisk

0th

Percentile

##### Cross Validated Bandwidth Selection for Relative Risk Estimation

Uses cross-validation to select a smoothing bandwidth for the estimation of relative risk.

Keywords
methods, smooth, spatial
##### Usage
bw.relrisk(X, method = "likelihood", nh = 32)
##### Arguments
X
A multitype point pattern (object of class "ppp" which has factor valued marks).
method
Character string determining the cross-validation method. Current options are "likelihood", "leastsquares" or "weightedleastsquares".
nh
Number of trial values of smoothing bandwith sigma to consider.
##### Details

This function selects an appropriate bandwidth for the nonparametric estimation of relative risk using relrisk. Consider the indicators $y_{ij}$ which equal $1$ when data point $x_i$ belongs to type $j$, and equal $0$ otherwise. For a particular value of smoothing bandwidth, let $\hat p_j(u)$ be the estimated probabilities that a point at location $u$ will belong to type $j$. Then the bandwidth is chosen to minimise either the likelihood, the squared error, or the approximately standardised squared error, of the indicators $y_{ij}$ relative to the fitted values $\hat p_j(x_i)$. See Diggle (2003).

The result is a numerical value giving the selected bandwidth sigma. The result also belongs to the class "bw.relrisk" allowing it to be printed and plotted. The plot shows the cross-validation criterion as a function of bandwidth.

##### Value

• A numerical value giving the selected bandwidth. The result also belongs to the class "bw.relrisk".

##### References

Diggle, P.J. (2003) Statistical analysis of spatial point patterns, Second edition. Arnold.

relrisk

• bw.relrisk
##### Examples
data(urkiola)
b <- bw.relrisk(urkiola)
b
plot(b)
Documentation reproduced from package spatstat, version 1.23-2, License: GPL (>= 2)

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