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Asymptotic normality of the maximum likelihood estimator for cooperative sequential adsorption

  • Mathew D. Penrose (a1) and Vadim Shcherbakov (a2)
Abstract

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.

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Copyright
Corresponding author
Postal address: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. Email address: masmdp@bath.ac.uk
∗∗ Postal address: Laboratory of Large Random Systems, Faculty of Mechanics and Mathematics, Moscow State University, Glavnoe Zdanie, Leninskie Gory, Moscow, 119991, Russia. Email address: v.shcherbakov@mech.math.msu.su
References
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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, 518532.
[2] Billingsley P. (1968). Convergence of Probability Measures. John Wiley, New York.
[3] Evans J. W. (1993). Random and cooperative sequential adsorption. Rev. Mod. Phys. 65, 12811329.
[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.
[5] Lehmann E. L. (1983). Theory of Point Estimation. John Wiley, New York.
[6] Løcherbach E. and Orlandi E. (2011). Neighborhood radius estimation for variable-neighborhood random fields. Preprint. Available at http://arxiv.org/abs/1002.4850v5.
[7] McLeish D. L. (1974). Dependent central limit theorems and invariance principles. Ann. Prob. 2, 620628
[8] Møller J. and Waagepetersen R. P. (2004). Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC, Boca Raton, FL.
[9] Penrose M. D. and Shcherbakov V. (2009). Maximum likelihood estimation for cooperative sequential adsorption. Adv. Appl. Prob. 41, 9781001.
[10] Rafelski S. M. and Marshall W. F. (2008). Building the cell: design principles of cellular architecture. Nature Rev. Mol. Cell Biol. 9, 593602.
[11] Shcherbakov V. (2006). Limit theorems for random point measures generated by cooperative sequential adsorption. J. Statist. Phys. 124, 14251441.
[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, 24362448.
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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