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Estimation of parameters in a network reliability model with spatial dependence

Published online by Cambridge University Press:  15 November 2005

Ian Hepburn Dinwoodie
Ian Hepburn Dinwoodie*
Affiliation:
ISDS, Box 90251, Duke University, Durham NC 27708, USA; ihd@stat.duke.edu
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Abstract

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.

Keywords

Curie-WeissEM-algorithmiterative proportional scalingmaximum likelihoodnetwork tomography.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 9 , February 2005 , pp. 241 - 253
Copyright
© EDP Sciences, SMAI, 2005

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References

O. Barndorff-Nielsen, Information and Exponential Families. Wiley, New York (1978).
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).
Cáceres, R., Duffield, N.G., Horowitz, J., Towsley, D. and Multicast-based, T. Bu inference of network internal characteristics: accuracy of packet loss estimation. IEEE Trans. Inform. Theory 45 (2000) 2462–2480.
Coates, M., Hero, A.O., Nowak, R. and Internet, B. Yu tomography. IEEE Signal Processing Magazine 19 (2002) 47–65. CrossRef
Darroch, J.N. and Ratcliff, D., Generalized iterative scaling for log-linear models. Ann. Math. Stat. 43 (1972) 1470–1480. CrossRef
Dempster, A.P., Laird, N.M. and Rubin, D.B., Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. B 39 (1997) 1–38.
Dinwoodie, I.H. and Mosteig, E., Statistical inference for network reliability with spatial dependence. SIAM J. Discrete Math. 16 (2003) 663–674. CrossRef
Duffield, N., Horowitz, J., Towsley, D., Wei, W. and Friedman, T., Multicast-based loss inference with missing data. IEEE J. Selected Areas Communications 20 (2002) 700–713. CrossRef
Ji, C. and Elwalid, A., Measurement-based network monitoring and inference: scalability and missing information. IEEE J. Selected Areas Communications 20 (2002) 714–725.
Liang, G. and Maximum, B. Yu pseudo-likelihood estimation in network tomography. IEEE Trans. Signal Process. 51 (2003) 2043–2053. CrossRef
M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacon, Boston (1964).
P. Parrilo and B. Sturmfels, Minimizing polynomial functions. http://xyz.lanl.gov/abs/math.OC/0103170 (2002).
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.
Jeff Wu, C.F., On the convergence of the EM algorithm. Ann. Statist. 11 (1983) 95–103.
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).