Nonparametric inference for Poisson-Laguerre tessellations
T.F.W. van der Jagt (TU Delft - Statistics)
G Jongbloed (TU Delft - Statistics)
Martina Vittorietti (TU Delft - Statistics)
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Abstract
In this paper, we consider statistical inference for Poisson-Laguerre tessellations in (Formula presented.). The object of interest is a distribution function (Formula presented.) which describes the distribution of the arrival times of the generator points. The function (Formula presented.) uniquely determines the intensity measure of the underlying Poisson process. Two nonparametric estimators for (Formula presented.) are introduced, which depend only on the points of the Poisson process that generate non-empty cells and the actual cells corresponding to these points. The proposed estimators are proven to be strongly consistent as the observation window expands unboundedly to the whole space. We also consider a stereological setting, where one is interested in estimating the distribution function associated with the Poisson process of a higher-dimensional Poisson-Laguerre tessellation, given that a corresponding sectional Poisson-Laguerre tessellation is observed.
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