6533b82dfe1ef96bd1291547

RESEARCH PRODUCT

Some properties of local weighted second-order statistics for spatio-temporal point processes

Giada AdelfioFrancisco J. Rodríguez-cortésMarianna SiinoJorge Mateu

subject

Environmental Engineeringsecond-order characteristics010504 meteorology & atmospheric sciencesComputer science0208 environmental biotechnologyresidual analysisInverseComputational intelligence02 engineering and technology01 natural sciencesPoint processSecond order statisticslocal propertiesEnvironmental ChemistryApplied mathematicsSafety Risk Reliability and Quality0105 earth and related environmental sciencesGeneral Environmental ScienceWater Science and TechnologyHomogeneity (statistics)Intensity function020801 environmental engineeringWeightingK-functionspatio-temporal point patternsSettore SECS-S/01 - StatisticaK-function Local properties Residual analysis Second-order characteristics Spatio-temporal point patterns

description

Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data into residuals as a result of a thinning or a rescaling procedure. We alternatively consider here second-order statistics coming from weighted measures. Motivated by Adelfio and Schoenberg (Ann Inst Stat Math 61(4):929–948, 2009) for the temporal and spatial cases, we consider an extension to the spatio-temporal context in addition to focussing on local characteristics. In particular, our proposed method assesses goodness-of-fit of spatio-temporal models by using local weighted second-order statistics, computed after weighting the contribution of each observed point by the inverse of the conditional intensity function that identifies the process. Weighted second-order statistics directly apply to data without assuming homogeneity nor transforming the data into residuals, eliminating thus the sampling variability due to the use of a transforming procedure. We provide some characterisations and show a number of simulation studies.

yearjournalcountryeditionlanguage
2019-11-21Stochastic Environmental Research and Risk Assessment
https://doi.org/10.1007/s00477-019-01748-1