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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Abstract

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

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

Dates
First available in Project Euclid: 30 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.aap/1377868532

Digital Object Identifier
doi:10.1239/aap/1377868532

Mathematical Reviews number (MathSciNet)
MR3102465

Zentralblatt MATH identifier
1292.60015

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

Keywords
Dimension reduction central subspace random marked set Gaussian random field covariate

Citation

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. https://projecteuclid.org/euclid.aap/1377868532


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