Asymptotic normality of the maximum likelihood estimator for cooperative sequential adsorption. (English) Zbl 1235.62025

Penrose, Mathew D.; Shcherbakov, Vadim

Adv. Appl. Probab. 43, No. 3, 636-648 (2011).

Summary: 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.

MSC:

62F12	Asymptotic properties of parametric estimators
62M30	Inference from spatial processes
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
60K35	Interacting random processes; statistical mechanics type models; percolation theory
62L99	Sequential statistical methods
65C60	Computational problems in statistics (MSC2010)

Keywords:

time series of spatial locations; spatial random growth; maximum likelihood estimation; Fisher information; martingale; thermodynamic limit

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