Planar Segment Processes with Reference Mark Distributions, Modeling and Estimation

Viktor Beneš (), Jakub Večeřa () and Milan Pultar ()
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Viktor Beneš: Charles University, Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics
Jakub Večeřa: Charles University, Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics
Milan Pultar: Charles University, Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 3, 683-698

Abstract: Abstract The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide with the corresponding observed distributions. Statistical methods are presented which first estimate scalar parameters by known approaches and then the reference distribution is estimated non-parametrically. Besides a general theory we offer two models, first a Gibbs type segment process with reference directional distribution and secondly an inhomogeneous process with reference length distribution. The estimation is demonstrated in simulation studies where the variability of estimators is presented graphically.

Keywords: Conditional intensity; Segment process; Semiparametric estimation; MSC 60D05; MSC 60G55 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11009-017-9608-x

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