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

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)
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[1] Beil, M. et al. (2009). Simulating the formation of keratin filament networks by a piecewise-deterministic Markov process. J. Theoret. Biol. , 256, 518-532. · Zbl 1400.92160
[2] Billingsley, P. (1968). Convergence of Probability Measures. John Wiley, New York. · Zbl 0172.21201
[3] Evans, J. W. (1993). Random and cooperative sequential adsorption. Rev. Mod. Phys. 65, 1281-1329.
[4] Galves, A., Orlandi, E. and Takahashi, D. Y. (2010). Identifying interacting pairs of sites in infinite range Ising models. Preprint. Available at http://arxiv.org/abs/1006.0272v2. · Zbl 1316.60145
[5] Lehmann, E. L. (1983). Theory of Point Estimation . John Wiley, New York. · Zbl 0522.62020
[6] Løcherbach, E. and Orlandi, E. (2011). Neighborhood radius estimation for variable-neighborhood random fields. Preprint. Available at http://arxiv.org/abs/1002.4850v5. · Zbl 1398.62058
[7] McLeish, D. L. (1974). Dependent central limit theorems and invariance principles. Ann. Prob. 2, 620-628 · Zbl 0287.60025
[8] Møller, J. and Waagepetersen, R. P. (2004). Statistical Inference and Simulation for Spatial Point Processes . Chapman and Hall/CRC, Boca Raton, FL. · Zbl 1044.62101
[9] Penrose, M. D. and Shcherbakov, V. (2009). Maximum likelihood estimation for cooperative sequential adsorption. Adv. Appl. Prob. 41, 978-1001. · Zbl 1186.62115
[10] Rafelski, S. M. and Marshall, W. F. (2008). Building the cell: design principles of cellular architecture. Nature Rev. Mol. Cell Biol. 9, 593-602.
[11] Shcherbakov, V. (2006). Limit theorems for random point measures generated by cooperative sequential adsorption. J. Statist. Phys. 124, 1425-1441. · Zbl 1151.82376
[12] Windoffer, R., Wöll, S., Strnad, P. and Leube, R. E. (2004). Identification of novel principles of keratin filament network turnover in living cells. Mol. Biol. Cell 15, 2436-2448.
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