Estimation of parameters in a network reliability model with spatial dependence
ESAIM: Probability and Statistics, Tome 9 (2005), pp. 241-253.

An iterative method based on a fixed-point property is proposed for finding maximum likelihood estimators for parameters in a model of network reliability with spatial dependence. The method is shown to converge at a geometric rate under natural conditions on data.

DOI : https://doi.org/10.1051/ps:2005012
Classification : 62B05,  62F10
Mots clés : Curie-Weiss, EM-algorithm, iterative proportional scaling, maximum likelihood, network tomography
@article{PS_2005__9__241_0,
     author = {Dinwoodie, Ian Hepburn},
     title = {Estimation of parameters in a network reliability model with spatial dependence},
     journal = {ESAIM: Probability and Statistics},
     pages = {241--253},
     publisher = {EDP-Sciences},
     volume = {9},
     year = {2005},
     doi = {10.1051/ps:2005012},
     zbl = {1136.62380},
     mrnumber = {2167326},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps:2005012/}
}
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Dinwoodie, Ian Hepburn. Estimation of parameters in a network reliability model with spatial dependence. ESAIM: Probability and Statistics, Tome 9 (2005), pp. 241-253. doi : 10.1051/ps:2005012. http://www.numdam.org/articles/10.1051/ps:2005012/

[1] O. Barndorff-Nielsen, Information and Exponential Families. Wiley, New York (1978). | MR 489333

[2] T. Bu, N. Duffield, F. Lo Presti and D. Towsley, Network tomography on general topologies. Proc. ACM Sigmetrics 2002, Marina Del Ray, June 15-19 (2002).

[3] R. Cáceres, N.G. Duffield, J. Horowitz, D. Towsley and T. Bu, Multicast-based inference of network internal characteristics: accuracy of packet loss estimation. IEEE Trans. Inform. Theory 45 (2000) 2462-2480. | Zbl 0961.94002

[4] M. Coates, A.O. Hero, R. Nowak and B. Yu, Internet tomography. IEEE Signal Processing Magazine 19 (2002) 47-65.

[5] J.N. Darroch and D. Ratcliff, Generalized iterative scaling for log-linear models. Ann. Math. Stat. 43 (1972) 1470-1480. | Zbl 0251.62020

[6] A.P. Dempster, N.M. Laird and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. B 39 (1997) 1-38. | Zbl 0364.62022

[7] I.H. Dinwoodie and E. Mosteig, Statistical inference for network reliability with spatial dependence. SIAM J. Discrete Math. 16 (2003) 663-674. | Zbl 1047.62094

[8] N. Duffield, J. Horowitz, D. Towsley, W. Wei and T. Friedman, Multicast-based loss inference with missing data. IEEE J. Selected Areas Communications 20 (2002) 700-713.

[9] C. Ji and A. Elwalid, Measurement-based network monitoring and inference: scalability and missing information. IEEE J. Selected Areas Communications 20 (2002) 714-725.

[10] G. Liang and B. Yu, Maximum pseudo-likelihood estimation in network tomography. IEEE Trans. Signal Process. 51 (2003) 2043-2053.

[11] M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacon, Boston (1964). | MR 162808 | Zbl 0126.02404

[12] P. Parrilo and B. Sturmfels, Minimizing polynomial functions. http://xyz.lanl.gov/abs/math.OC/0103170 (2002). | MR 1995016

[13] Y. Tsang, M. Coates and R. Nowak, Passive network tomography using EM algorithms. Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, Utah 3 (May 2001) 1469-1472.

[14] C.F. Jeff Wu, On the convergence of the EM algorithm. Ann. Statist. 11 (1983) 95-103. | Zbl 0517.62035

[15] B. Xi, G. Michailidis and V.N. Nair, Estimating network internal losses using a new class of probing experiments. University of Michigan Department of Statistics Technical Report 397 (2003).

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