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The Autocovariance Function for Marked Point Processes: A Comparison between Two Different Approaches
Author(s) -
Capobianco Rosa,
Renshaw Eric
Publication year - 1998
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/(sici)1521-4036(199808)40:4<431::aid-bimj431>3.0.co;2-v
Subject(s) - autocovariance , estimator , mathematics , disjoint sets , bandlimiting , point process , fourier transform , isotropy , lattice (music) , statistical physics , algorithm , mathematical analysis , statistics , physics , quantum mechanics , acoustics
Exploratory analysis of marked point patterns has previously been conducted using two disjoint techniques, namely the mark correlation function and spectral analysis. Our purpose here is to present two alternative autocovariance estimators to the mark correlation function which not only apply in both planar and lattice situations, but which in the lattice case can also be considered in terms of the inverse Fourier transform of the spectrum. Moreover, they can be applied to isotropic or anisotropic marked point patterns. Various examples are presented to show how these estimators perform when applied to data sets possessing different kinds of mark structure, and a rank test procedure is proposed to enable the construction of empirical tests of hypothesis.