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Sliced Inverse Regression and Independence in Random Marked Sets with Covariates

Part of: Geometric probability and stochastic geometry Inference from stochastic processes

Published online by Cambridge University Press:  04 January 2016

Ondřej Šedivý ,
Jakub Stanek ,
Blažena Kratochvílová  and
Viktor Beneš
Ondřej Šedivý*
Affiliation:
Charles University in Prague
Jakub Stanek*
Affiliation:
Charles University in Prague
Blažena Kratochvílová*
Affiliation:
Palacký University Olomouc
Viktor Beneš*
Affiliation:
Charles University in Prague
*
∗ Postal address: Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Charles University in Prague, Sokolovská 83, 18675 Praha 8, Czech Republic.
∗∗∗ Postal address: Faculty of Mathematics and Physics, Department of Mathematics Education, Charles University in Prague, Sokolovská 83, 18675 Praha 8, Czech Republic. Email address: stanekj@karlin.mff.cuni.cz
∗∗∗∗ Postal address: Faculty of Science, Department of Mathematical Analysis and Applications of Mathematics, 17. listopadu 12, 77146 Olomouc, Czech Republic. Email address: blaza.kratochvilova@gmail.com
∗ Postal address: Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Charles University in Prague, Sokolovská 83, 18675 Praha 8, Czech Republic.
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Abstract

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Dimension reduction of multivariate data was developed by Y. Guan for point processes with Gaussian random fields as covariates. The generalization to fibre and surface processes is straightforward. In inverse regression methods, we suggest slicing based on geometrical marks. An investigation of the properties of this method is presented in simulation studies of random marked sets. In a refined model for dimension reduction, the second-order central subspace is analyzed in detail. A real data pattern is tested for independence of a covariate.

Keywords

Dimension reductioncentral subspacerandom marked setGaussian random fieldcovariate

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 45 , Issue 3 , September 2013 , pp. 626 - 644
Copyright
© Applied Probability Trust 

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