Inhomogeneous higher-order summary statistics for point processes on linear networks

• As a workaround for the lack of transitive transformations on linear network structures, which are required to consider different notions of distributional invariance, including stationarity, we introduce the notions of pseudostationarity and intensity reweighted moment pseudostationarity for point processes on linear networks. Moreover, using arbitrary so-called regular linear network distances, e.g. the Euclidean and the shortest-path distance, we further propose geometrically corrected versions of different higher-order summary statistics, including the inhomogeneous empty space function, the inhomogeneous nearest neighbour distance distribution function and the inhomogeneous J-function. Such summary statistics detect interactions of order higher than two. We also discuss their nonparametric estimators and through a simulation study, considering models with different types of spatial interaction and different networks, we study the performance of our proposed summary statistics by means of envelopes. Our summary statistic estimators manage to capture clustering, regularity as well as Poisson process independence. Finally, we make use of our new summary statistics to analyse two different datasets: motor vehicle traffic accidents and spiderwebs.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Sciences (hsv//eng)

Nyckelord

Inhomogeneous linear empty space function

Inhomogeneous linear J -function

Inhomogeneous linear nearest neighbour distance distribution function

Linear network

Pseudostationarity

Regular distance metric

Traffic accident data

Inhomogeneous linear empty space function

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