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Fast Kernel Smoothing of Point Patterns on a Large Network using Two‐dimensional Convolution
Author(s) -
Rakshit Suman,
Davies Tilman,
Moradi M. Mehdi,
McSwiggan Greg,
Nair Gopalan,
Mateu Jorge,
Baddeley Adrian
Publication year - 2019
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12327
Subject(s) - smoothing , estimator , kernel smoother , kernel (algebra) , algorithm , convolution (computer science) , efficiency , mathematics , bandwidth (computing) , variance (accounting) , computer science , fourier transform , variable kernel density estimation , statistics , mathematical optimization , kernel method , artificial intelligence , mathematical analysis , telecommunications , artificial neural network , accounting , combinatorics , radial basis function kernel , support vector machine , business
Summary 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.