This is it! The revised version of a paper written with Arthur Charpentier has been submitted yesterday! It is untitled « Kernel Density Estimation with Ripley’s Circumferential Correction ». Here is the abstract:
« In this paper, we investigate (and extend) Ripley’scircumference method to correct bias of density estimation of edges (or frontiers) of regions. The idea of the method was theoretical and difficult to implement. We provide a simple technique – based of properties of Gaussian kernels – to efficiently compute weights to correct border bias on frontiers of the region of interest, with an automatic selection of an optimal radius for the method. We illustrate the use of that technique to visualize hot spots of car accidents and campsite locations, as well as location of bike thefts. »
The paper is available on https://hal.archives-ouvertes.fr/hal-00725090.
In this revised version, we added some applications, and some new maps.
Last time, we uploaded some explainations on Arthur’s blog, and on mine as well. This time, we did something a bit different. The R code (which explains the technique used to compute the estimates and offers a way to plot the results on a map) is available on a Github repository : https://github.com/ripleyCorr/Kernel_density_ripley. An html page is also available: http://egallic.fr/R/sKDE/smooth-maps/kde.html.
@freakonometrics also published a post on his blog: http://freakonometrics.hypotheses.org/17486.