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.
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},
mrnumber = {2167326},
zbl = {1136.62380},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps:2005012/}
}
TY - JOUR AU - Dinwoodie, Ian Hepburn TI - Estimation of parameters in a network reliability model with spatial dependence JO - ESAIM: Probability and Statistics PY - 2005 SP - 241 EP - 253 VL - 9 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps:2005012/ DO - 10.1051/ps:2005012 LA - en ID - PS_2005__9__241_0 ER -
%0 Journal Article %A Dinwoodie, Ian Hepburn %T Estimation of parameters in a network reliability model with spatial dependence %J ESAIM: Probability and Statistics %D 2005 %P 241-253 %V 9 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps:2005012/ %R 10.1051/ps:2005012 %G en %F PS_2005__9__241_0
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://archive.numdam.org/articles/10.1051/ps:2005012/
[1] , Information and Exponential Families. Wiley, New York (1978). | MR
[2] ,, and, Network tomography on general topologies. Proc. ACM Sigmetrics 2002, Marina Del Ray, June 15-19 (2002).
[3] ,,, and, Multicast-based inference of network internal characteristics: accuracy of packet loss estimation. IEEE Trans. Inform. Theory 45 (2000) 2462-2480. | Zbl
[4] ,, and, Internet tomography. IEEE Signal Processing Magazine 19 (2002) 47-65.
[5] and, Generalized iterative scaling for log-linear models. Ann. Math. Stat. 43 (1972) 1470-1480. | Zbl
[6] , and, Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. B 39 (1997) 1-38. | Zbl
[7] and, Statistical inference for network reliability with spatial dependence. SIAM J. Discrete Math. 16 (2003) 663-674. | Zbl
[8] ,,, and, Multicast-based loss inference with missing data. IEEE J. Selected Areas Communications 20 (2002) 700-713.
[9] and, Measurement-based network monitoring and inference: scalability and missing information. IEEE J. Selected Areas Communications 20 (2002) 714-725.
[10] and, Maximum pseudo-likelihood estimation in network tomography. IEEE Trans. Signal Process. 51 (2003) 2043-2053.
[11] and, A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacon, Boston (1964). | MR | Zbl
[12] and, Minimizing polynomial functions. http://xyz.lanl.gov/abs/math.OC/0103170 (2002). | MR
[13] , and, 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] , On the convergence of the EM algorithm. Ann. Statist. 11 (1983) 95-103. | Zbl
[15] , and, Estimating network internal losses using a new class of probing experiments. University of Michigan Department of Statistics Technical Report 397 (2003).
Cité par Sources :
