Kernel Density Estimation on a Linear Network

This paper develops a statistically principled approach to kernel density estimation on a network of lines, such as a road network. Existing heuristic techniques are reviewed, and their weaknesses are identified. The correct analogue of the Gaussian kernel is the 'heat kernel', the occupat...

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Bibliographic Details
Published in:Scandinavian journal of statistics 2017-06, Vol.44 (2), p.324-345
Main Authors: MCSWIGGAN, GREG, BADDELEY, ADRIAN, NAIR, GOPALAN
Format: Article
Language:English
Subjects:
Accident data
Algorithms
bandwidth selection
Brownian motion
Density
Diffusion
equal‐split kernels
Estimating techniques
finite difference algorithm
heat equation
heat kernel
Heuristic
intensity
International
Kernels
Network topologies
road accidents
Roads
spatial point process
Statistical analysis
Studies
Thermodynamics
Time dependence
Traffic accidents
Traffic accidents & safety
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Summary:This paper develops a statistically principled approach to kernel density estimation on a network of lines, such as a road network. Existing heuristic techniques are reviewed, and their weaknesses are identified. The correct analogue of the Gaussian kernel is the 'heat kernel', the occupation density of Brownian motion on the network. The corresponding kernel estimator satisfies the classical time-dependent heat equation on the network. This 'diffusion estimator' has good statistical properties that follow from the heat equation. It is mathematically similar to an existing heuristic technique, in that both can be expressed as sums over paths in the network. However, the diffusion estimate is an infinite sum, which cannot be evaluated using existing algorithms. Instead, the diffusion estimate can be computed rapidly by numerically solving the time-dependent heat equation on the network. This also enables bandwidth selection using cross-validation. The diffusion estimate with automatically selected bandwidth is demonstrated on road accident data.
ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12255