Maximum likelihood estimation for cooperative sequential adsorption

Maximum likelihood estimation for cooperative sequential adsorption

Mathew D. Penrose and Vadim Shcherbakov

Source: Adv. in Appl. Probab. Volume 41, Number 4 (2009), 978-1001.

Abstract

We consider a model for a time series of spatial locations, in which points are placed sequentially at random into an initially empty region of ℝ^d, and given the current configuration of points, the likelihood at location x for the next particle is proportional to a specified function β_k of the current number (k) of points within a specified distance of x. We show that the maximum likelihood estimator of the parameters β_k (assumed to be zero for k exceeding some fixed threshold) is consistent in the thermo\-dynamic limit where the number of points grows in proportion to the size of the region.

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Primary Subjects: 62M30, 60K35

Secondary Subjects: 60D05

Keywords: Cooperative sequential adsorption; space--time point process; maximum likelihood estimation; thermodynamic limit; increasing domain asymptotic; law of large numbers

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aap/1261669581
Digital Object Identifier: doi:10.1239/aap/1261669581
Zentralblatt MATH identifier: 1186.62115
Mathematical Reviews number (MathSciNet): MR2663231

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