Advances in Applied Probability

Sliced inverse regression and independence in random marked sets with covariates

Ondřej} Šedivý, Jakub Stanek, Blažena Kratochvílová, and Viktor Beneš

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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.

Article information

Adv. in Appl. Probab., Volume 45, Number 3 (2013), 626-644.

First available in Project Euclid: 30 August 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 62M30: Spatial processes

Dimension reduction central subspace random marked set Gaussian random field covariate


Šedivý, Ondřej}; Stanek, Jakub; Kratochvílová, Blažena; Beneš, Viktor. Sliced inverse regression and independence in random marked sets with covariates. Adv. in Appl. Probab. 45 (2013), no. 3, 626--644. doi:10.1239/aap/1377868532.

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