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).
|Qualification||Doctor of Philosophy|
|Award date||21 Nov 2018|
|Publication status||Published - 21 Nov 2018|
- Adaptive estimator
- Intensity estimator
- Linear network
- Point process