Fast Kernel Smoothing of Point Patterns on a Large Network using Two-dimensional Convolution

Suman Rakshit, Tilman Davies, M. Mehdi Moradi, Greg McSwiggan, Gopalan Nair, Jorge Mateu, Adrian Baddeley

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We propose a computationally efficient and statistically principled method for kernel smoothing of point pattern data on a linear network. The point locations, and the network itself, are convolved with a two-dimensional kernel and then combined into an intensity function on the network. This can be computed rapidly using the fast Fourier transform, even on large networks and for large bandwidths, and is robust against errors in network geometry. The estimator is consistent, and its statistical efficiency is only slightly suboptimal. We discuss bias, variance, asymptotics, bandwidth selection, variance estimation, relative risk estimation and adaptive smoothing. The methods are used to analyse spatially varying frequency of traffic accidents in Western Australia and the relative risk of different types of traffic accidents in Medellín, Colombia.

Original languageEnglish
JournalInternational Statistical Review
DOIs
Publication statusE-pub ahead of print - 6 Jun 2019

Fingerprint Dive into the research topics of 'Fast Kernel Smoothing of Point Patterns on a Large Network using Two-dimensional Convolution'. Together they form a unique fingerprint.

Cite this