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Detecting dependence between marks and locations of marked point processes
Author(s) -
Schlather Martin,
Ribeiro Paulo J.,
Diggle Peter J.
Publication year - 2004
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1046/j.1369-7412.2003.05343.x
Subject(s) - point process , point (geometry) , mathematics , isotropy , conditional variance , variance (accounting) , statistical physics , statistics , combinatorics , econometrics , physics , geometry , optics , economics , volatility (finance) , accounting , autoregressive conditional heteroskedasticity
Summary. We introduce two characteristics for stationary and isotropic marked point proces‐ ses, E ( h ) and V ( h ), and describe their use in investigating mark–point interactions. These quantities are functions of the interpoint distance h and denote the conditional expectation and the conditional variance of a mark respectively, given that there is a further point of the process a distance h away. We present tests based on E and V for the hypothesis that the values of the marks can be modelled by a random field which is independent of the unmarked point process. We apply the methods to two data sets in forestry.