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Asymptotic normality of the maximum likelihood estimator for cooperative sequential adsorption

Part of: Inference from stochastic processes Special processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Mathew D. Penrose  and
Vadim Shcherbakov
Mathew D. Penrose*
Affiliation:
University of Bath
Vadim Shcherbakov*
Affiliation:
Moscow State University
*
∗ Postal address: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. Email address: [email protected]
∗∗ Postal address: Laboratory of Large Random Systems, Faculty of Mechanics and Mathematics, Moscow State University, Glavnoe Zdanie, Leninskie Gory, Moscow, 119991, Russia. Email address: [email protected]
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Abstract

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We consider statistical inference for a parametric cooperative sequential adsorption model for spatial time series data, based on maximum likelihood. We establish asymptotic normality of the maximum likelihood estimator in the thermodynamic limit. We also perform and discuss some numerical simulations of the model, which illustrate the procedure for creating confidence intervals for large samples.

Keywords

Cooperative sequential adsorptiontime series of spatial locationsspatial random growthmaximum likelihood estimationasymptotic normalityFisher informationmartingalethermodynamic limit

MSC classification

Primary: 62M30: Spatial processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 43 , Issue 3 , September 2011 , pp. 636 - 648
Copyright
Copyright © Applied Probability Trust 2011 

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