TY - JOUR

T1 - Maximum likelihood estimation for cooperative sequential adsorption

AU - Penrose, M D

AU - Shcherbakov, Vadim

PY - 2009/12

Y1 - 2009/12

N2 - 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 beta(k) of the current number (k) of points within a specified distance of x. We show that the maximum likelihood estimator of the parameters beta(k) (assumed to be zero for k exceeding some fixed threshold) is consistent in the thermodynamic limit where the number of points grows in proportion to the size of the region.

AB - 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 beta(k) of the current number (k) of points within a specified distance of x. We show that the maximum likelihood estimator of the parameters beta(k) (assumed to be zero for k exceeding some fixed threshold) is consistent in the thermodynamic limit where the number of points grows in proportion to the size of the region.

UR - http://www.scopus.com/inward/record.url?scp=77949309882&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1239/aap/1261669581

U2 - 10.1239/aap/1261669581

DO - 10.1239/aap/1261669581

M3 - Article

SN - 0001-8678

VL - 41

SP - 978

EP - 1001

JO - Advances in Applied Probability

JF - Advances in Applied Probability

IS - 4

ER -