Displaying similar documents to “Limit theorems for multi-dimensional random quantizers.”

Moderate deviations for some point measures in geometric probability

Yu Baryshnikov, P. Eichelsbacher, T. Schreiber, J. E. Yukich (2008)

Annales de l'I.H.P. Probabilités et statistiques

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Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy moderate deviation principles. This leads to moderate deviation principles and laws of the iterated logarithm for random packing models as well as for statistics associated with germ-grain models and nearest neighbor graphs.

Process level moderate deviations for stabilizing functionals

Peter Eichelsbacher, Tomasz Schreiber (2010)

ESAIM: Probability and Statistics

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Functionals of spatial point process often satisfy a weak spatial dependence condition known as . In this paper we prove process level moderate deviation principles (MDP) for such functionals, which is a level-3 result for empirical point fields as well as a level-2 result for empirical point measures. The level-3 rate function coincides with the so-called specific information. We show that the general result can be applied to prove MDPs for various particular functionals, including...