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Spatial and spatio-temporal point patterns on linear networks
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Orientador(es)
Resumo(s)
The last decade witnessed an extraordinary increase in interest in the analysis
of network related data and trajectories. This pervasive interest is partly caused
by a strongly expanded availability of such datasets. In the spatial statistics field,
there are numerous real examples such as the locations of traffic accidents and
geo-coded locations of crimes in the streets of cities that need to restrict the
support of the underlying process over such linear networks to set and define a
more realistic scenario. Examples of trajectories are the path taken by moving
objects such as taxis, human beings, animals, etc.
Intensity estimation on a network of lines, such as a road network, seems to
be a surprisingly complicated task. Several techniques published in the literature,
in geography and computer science, have turned out to be erroneous. We
propose several adaptive and non-adaptive intensity estimators, based on kernel
smoothing and Voronoi tessellation. Theoretical properties such as bias, variance,
asymptotics, bandwidth selection, variance estimation, relative risk estimation,
and adaptive smoothing are discussed. Moreover, their statistical performance is
studied through simulation studies and is compared with existing methods.
Adding the temporal component, we also consider spatio-temporal point patterns
with spatial locations restricted to a linear network. We present a nonparametric
kernel-based intensity estimator and develop second-order characteristics
of spatio-temporal point processes on linear networks such as K-function
and pair correlation function to analyse the type of interaction between points.
In terms of trajectories, we introduce the R package trajectories that contains
different classes and methods to handle, summarise and analyse trajectory data.
Simulation and model fitting, intensity estimation, distance analysis, movement
smoothing, Chi maps and second-order summary statistics are discussed. Moreover, we analyse different real datasets such as a crime data from Chicago
(US), anti-social behaviour in Castell´on (Spain), traffic accidents in Medell´ın
(Colombia), traffic accidents in Western Australia, motor vehicle traffic accidents
in an area of Houston (US), locations of pine saplings in a Finnish forest, traffic
accidents in Eastbourne (UK) and one week taxi movements in Beijing (China).
Descrição
A thesis submitted in partial fulfillment of the requirements for the degree of Doctor in Information Management, specialization in Geographic Information Systems
Palavras-chave
Adaptive estimator Intensity estimator Kernel Linear network, Point process Resample-smoothing Trajectory Voronoi