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

2 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

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Kernel Smoothing
Convolution
Relative Risk
Accidents
Adaptive Smoothing
Traffic
Bandwidth Selection
Point Location
Intensity Function
Variance Estimation
Asymptotic Variance
Fast Fourier transform
Bandwidth
Kernel smoothing
kernel
Estimator

Cite this

Rakshit, Suman ; Davies, Tilman ; Moradi, M. Mehdi ; McSwiggan, Greg ; Nair, Gopalan ; Mateu, Jorge ; Baddeley, Adrian. / Fast Kernel Smoothing of Point Patterns on a Large Network using Two-dimensional Convolution. In: International Statistical Review. 2019.
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Fast Kernel Smoothing of Point Patterns on a Large Network using Two-dimensional Convolution. / Rakshit, Suman; Davies, Tilman; Moradi, M. Mehdi; McSwiggan, Greg; Nair, Gopalan; Mateu, Jorge; Baddeley, Adrian.

In: International Statistical Review, 06.06.2019.

Research output: Contribution to journalArticle

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