Estimation of parameters in a network reliability model with spatial dependence

Ian Hepburn Dinwoodie

ESAIM: Probability and Statistics (2010)

  • Volume: 9, page 241-253
  • ISSN: 1292-8100

Abstract

top
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.

How to cite

top

Dinwoodie, Ian Hepburn. "Estimation of parameters in a network reliability model with spatial dependence." ESAIM: Probability and Statistics 9 (2010): 241-253. <http://eudml.org/doc/104335>.

@article{Dinwoodie2010,
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. },
author = {Dinwoodie, Ian Hepburn},
journal = {ESAIM: Probability and Statistics},
keywords = {Curie-Weiss; EM-algorithm; iterative proportional scaling; maximum likelihood; network tomography.; network tomography},
language = {eng},
month = {3},
pages = {241-253},
publisher = {EDP Sciences},
title = {Estimation of parameters in a network reliability model with spatial dependence},
url = {http://eudml.org/doc/104335},
volume = {9},
year = {2010},
}

TY - JOUR
AU - Dinwoodie, Ian Hepburn
TI - Estimation of parameters in a network reliability model with spatial dependence
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 9
SP - 241
EP - 253
AB - 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.
LA - eng
KW - Curie-Weiss; EM-algorithm; iterative proportional scaling; maximum likelihood; network tomography.; network tomography
UR - http://eudml.org/doc/104335
ER -

References

top
  1. O. Barndorff-Nielsen, Information and Exponential Families. Wiley, New York (1978).  Zbl0387.62011
  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. Theory45 (2000) 2462–2480.  Zbl0961.94002
  4. M. Coates, A.O. Hero, R. Nowak and B. Yu, Internet tomography. IEEE Signal Processing Magazine19 (2002) 47–65.  
  5. J.N. Darroch and D. Ratcliff, Generalized iterative scaling for log-linear models. Ann. Math. Stat.43 (1972) 1470–1480.  Zbl0251.62020
  6. A.P. Dempster, N.M. Laird and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. B39 (1997) 1–38.  Zbl0364.62022
  7. I.H. Dinwoodie and E. Mosteig, Statistical inference for network reliability with spatial dependence. SIAM J. Discrete Math.16 (2003) 663–674.  Zbl1047.62094
  8. N. Duffield, J. Horowitz, D. Towsley, W. Wei and T. Friedman, Multicast-based loss inference with missing data. IEEE J. Selected Areas Communications20 (2002) 700–713.  
  9. C. Ji and A. Elwalid, Measurement-based network monitoring and inference: scalability and missing information. IEEE J. Selected Areas Communications20 (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).  Zbl0126.02404
  12. P. Parrilo and B. Sturmfels, Minimizing polynomial functions. (2002).  Zbl1099.13516URIhttp://xyz.lanl.gov/abs/math.OC/0103170
  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, Utah3 (May 2001) 1469–1472.  
  14. C.F. Jeff Wu, On the convergence of the EM algorithm. Ann. Statist.11 (1983) 95–103.  Zbl0517.62035
  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).  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.