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Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes

Influence of Edge Correction Methods and Intensity Estimates

Abstract

Non-parametric estimates of the K-function and the pair correlation function play a fundamental role for exploratory and explanatory analysis of spatial and spatio-temporal point patterns. These estimates usually require information from outside of the study region, resulting to the so-called edge effects which have to be corrected. They also depend on first-order characteristics, which have to be estimated in practice. In this paper, we extend classical edge correction methods to the spatio-temporal setting and compare the performance of the related estimators for stationary/non-stationary and/or isotropic/anisotropic point patterns. Further, we explore the influence of the estimated intensity function on these estimators.

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Correspondence to Edith Gabriel.

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Gabriel, E. Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes. Methodol Comput Appl Probab 16, 411–431 (2014). https://doi.org/10.1007/s11009-013-9358-3

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Keywords

  • Edge correction
  • Intensity estimation
  • Point process
  • Reduced second moment measure
  • Spatio-temporal data

AMS 2000 Subject Classification

  • 60G55
  • 62M30