Nonparametric copula density estimation in sensor networks

Proceedings - 2011 7th International Conference on Mobile Ad-hoc and Sensor Networks, MSN 2011

Volumn , Issue , 2011, Pages 1-8

  Qu, Leming ^a   Chen, Hao ^b   Tu, Yichen ^c  

^a BOISE STATE UNIVERSITY   (United States)

^b Boise State University   (United States)

^c University of South Florida   (United States)

Author keywords

copula; copula density estimation; dependence; sensor network

Indexed keywords

COPULA; COPULA DENSITY ESTIMATION; DENSITY ESTIMATION; DEPENDENCE; DISTRIBUTED DATA; FUSION CENTER; GRADIENT BASED ALGORITHM; LIKELIHOOD FUNCTIONS; LIMITED COMMUNICATION; LINEAR EQUALITY; MAXIMUM PENALIZED LIKELIHOOD; NON-PARAMETRIC; NUMERICAL EXPERIMENTS; PARAMETRIC FORMS; PRIVACY CONCERNS; QUADRATIC APPROXIMATION; QUADRATIC OPTIMIZATION PROBLEMS; REAL WORLD DATA; STATISTICAL DEPENDENCE; STATISTICAL LEARNING; TOTAL VARIATION;

ALGORITHMS; CONSTRAINED OPTIMIZATION; ESTIMATION; MAXIMUM LIKELIHOOD ESTIMATION; RANDOM VARIABLES; SENSOR NETWORKS;

MOBILE AD HOC NETWORKS;

EID: 84862932127     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/MSN.2011.50     Document Type: Conference Paper

References (55)

1. I. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, "A survey on sensor networks," IEEE Commun. Mag., vol. 40, no. 8, pp. 102-114, 2002.
2. A. Sklar, Fonctions de repartition à n dimensions et leurs marges, Publ. Inst. Stat. Univ. Paris, 1959.
3. P. Embrechts, F. Lindskog, and A. McNeil, "Modelling dependence with copulas and applications to risk management," in Handbook of Heavy Tailed Distributions in Finance, S. T. Rachev, Ed. North-Holland, Amserdam: Elsevier, 2003, ch. 8, pp. 329-384.
4. N. Kolve, U. dos Anjos, and B. Mendes, "Copulas: a review and recent developments," Stochastic Models, vol. 22, pp. 617-660, 2006.
5. T. Mikosch, "Copulas: tales and facts," Extremes, vol. 9, pp. 3-20, 2006.
6. P. Embrechts, "Copulas: a personal view," Journal of Risk and Insurance, vol. 76, pp. 639-650, 2009.
7. A. P., "Copula-based models for financial time series," in Handbook of Financial Time Series, T. Andersen, R. Davis, J.-P. Kreiss, and T. Mikosch, Eds. Verlag: Springer, 2009, pp. 767-785.
8. U. Cherubini, E. Luciano, and W. Vecchiato, Copula Methods in Finance. New York: John Wiley & Sons, 2004.
9. R. B. Nelsen, An Introduction to Copulas, 2nd ed., ser. Lecture Notes in Statistics. New York: Springer, 2006.
10. P. K. Trivedi and D. M. Zimmer, Copula Modeling: An Introduction for Practitioners. Hanover, Mass.: Now Publishers, 2007.
11. E. W. Frees and E. A. Valdez, "Understanding relationships using copulas," North American Actuarial Journal, vol. 2, pp. 1-25, 1998.
12. P. Embrechts, A. McNeil, and D. Straumann, "Correlation and dependence in risk management: Properties and pitfalls," in RISK Management: Value at Risk and Beyond, M. A. H. Dempster, Ed. Cambridge, U.K.: Cambridge University Press, 2002, pp. 176-223.
13. Y. Malevergne and D. Sornette, "Testing the gaussian copula hypothesis for financial assets dependence," Quant Fin, vol. 3, p. 231250, 2003.
14. M. Junker and A. May, "Measurement of aggregate risk with copulas,"Econ J, vol. 8, pp. 428-454, 2005.
15. J. Rodriguez, "Measuring financial contagion: a copula approach," J Empir Fin, vol. 41, pp. 401-423, 2007.
16. S. Chen and S. Poon, "Modelling international stock market contagion using copula and risk appetite," 2007, http://ssrn.com/abstract=1024288.
17. M. Davy and A. Doucet, "Copulas: A new insight into positive timefrequency distributions," IEEE Signal Process. Lett., vol. 10, no. 7, pp. 215-218, Jul. 2003.
18. N. Brunel, W. Pieczynski, and S. Derrode, "Copulas in vectorial hidden markov chains for multicomponent image segmentation," in Proc. ICASSP, 2005, pp. 717-720.
19. S. G. Iyengar, P. K. Varshney, and T. Damarla, "On the detection of footsteps using acoustic and seismic sensing," in Proc. Asilomar Conf. Signals, Syst. Comput., 2007, p. 22482252.
20. W. Ketchantang, S. Derrode, and L. Martin, "Pearson-based mixture model for color object tracking," Mach. Vis. Appl., vol. 19, pp. 457-466, 2008.
21. G. Mercier, G. Moser, and S. B. Serpico, "Conditional copulas for change detection in heterogeneous remote sensing images," IEEE Trans. Geosci. Remote Sens., vol. 46, no. 5, pp. 1428-1441, May 2008.
22. Y. Stitou, N. Lasmar, and Y. Berthoumieu, "Copula based multivariate gamma modeling for texture classification," in Proc. ICASSP, 2009, pp. 1045-1048.
23. T. Durrani and X. Zeng, "Copula-based divergence measures and their use in image registration," in EUSIPCO, 2009.
24. D.-B. Pougaza, A. Mohammad-Djafari, and J.-F. Bercher, "Link between copula and tomography," Pattern Recognition Letters, vol. 31, no. 14, pp. 2258-2264, Oct. 2010.
25. A. Sundaresan, A. Subramanian, P. K. Varshney, and T. Damarla, "A copula-based semi-parametric approach for footstep detection using seismic sensor networks," in Multisensor, Multisource Information Fusion: Architectures, Algorithms, and Applications, J. Braun, Ed. SPIE, 2010, p. 77100C, vol. 7710.
26. A. Sundaresan, P. Varshney, and N. Rao, "Copula-based fusion of correlated decisions," IEEE Trans. Aerosp. Electron. Syst., vol. 47, no. 1, pp. 454-471, Jan. 2011.
27. A. Sundaresan and P. Varshney, "Location estimation of a random signal source based on correlated sensor observations," IEEE Trans. Signal Process., vol. 59, no. 2, pp. 787-799, feb. 2011.
28. S. Iyengar, P. Varshney, and T. Damarla, "A parametric copula-based framework for hypothesis testing using heterogeneous data," IEEE Trans. Signal Process., vol. 59, no. 5, pp. 2308-2319, May 2011.
29. J. B. Predd, S. R. Kulkarni, and H. V. Poor, "Distributed learning in wireless sensor networks," IEEE Signal Process. Mag., pp. 56-69, Jul. 2006.
30. J. H. Shih and T. A. Louis, "Inferences on the association parameter in copula models for bivariate survival data," Biometrics, vol. 51, pp. 1384-1399, 1995.
31. B. Choros, R. Ibragimov, and E. Permiakova, "Copula estimation," in Copula Theory and Its Applications, Lecture Notes in Statistics, V198, Springer, 2010, pp. 77-91.
32. I. Gijbels and J. Mielniczuk, "Estimating the density of a copula function," Communications in Statistics - Theory and Methods, vol. 19, pp. 445-464, 1990.
33. J. Fermanian and O. Scaillet, "Nonparametric estimation of copulas for time series," vol. 5, no. 4, pp. 25-54, 2003.
34. Y. Malevergne and D. Sornette, Extreme Financial Risks. Heidelberg: Springer, 2006.
35. X. Shen, Y. Zhu, and L. Song, "Linear B-spline copulas with applications to nonparametric estimation of copulas," Computational Statistics & Data Analysis, vol. 52, pp. 3806-3819, 2008.
36. A. Sancetta and S. Satchell, "The Bernstein copula and its applications to modeling and approximations of multivariate distributions," Econometric Theory, vol. 20, pp. 535-562, 2004. (Pubitemid 38707270)
37. P. Hall and N. Neumeyer, "Estimating a bivariate density when there are extra data on one or both components," Biometrika, vol. 93, pp. 439-450, 2006. (Pubitemid 43992203)
38. C. Genest, E. Masiello, and K. Tribouley, "Estimating copula densities through wavelets," vol. 44, no. 2, pp. 170-181, Apr. 2009.
39. F. Autin, E. L. Pennecb, and K. Tribouley, "Thresholding methods to estimate the copula density," Journal of Multivariate Analysis, vol. 101, pp. 200-222, Jan. 2010.
40. L. Qu, Y. Qian, and H. Xie, "Copula density estimation by total variation penalized likelihood," Communications in Statistics - Simulation and Computation, vol. 38, no. 9, pp. 1891-1908, 2009.
41. L. Qu and W. Yin, "Copula density estimation by total variation penalized likelihood with linear equality constraints," CAAM, Rice University, Tech. Rep. TR09-40, 2009. [Online]. Available: http: /www.caam.rice.edu/~wy1/paperfiles/Rice CAAM TR09-40.PDF
42. T. Chan, A. Marquina, and P. Mulet, "High-order total variation-based image restoration," SIAM Journal on Scientific Computing, vol. 22, no. 2, pp. 503-516, 2000.
43. P. L. Combettes and J. C. Pesquet, "Image restoration subject to a total variation constraint," IEEE Trans. Image Process., vol. 13, no. 9, pp. 1213-1222, Sep. 2004.
44. A. Beck and M. Teboulle, "Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems," IEEE Trans. Image Process., vol. 18, no. 11, pp. 2419-2434, Nov. 2009.
45. -, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM Journal on Imaging Sciences, vol. 2, no. 1, pp. 183-202, 2009.
46. -, "Gradient-based algorithms with applications to signal recovery problems," in Convex Optimization in Signal Processing and Communications, D. P. Palomar and Y. C. Eldar, Eds. Cambridge university press, 2011, pp. 42-88.
47. J. Nocedal and S. Wright, Numerical Optimization, 2nd ed. New York: Springer, 2006.
48. S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, "Sparse reconstruction by separable approximation," IEEE Trans. Signal Process., vol. 57, no. 7, pp. 2479-2493, 2009.
49. J. J. Moreau, "Proximitet dualit dans un espace hilbertien," Bull. Soc. Math. France, vol. 93, pp. 273-299, 1965.
50. P. L. Combettes and V. R. Wajs, "Signal recovery by proximal forwardbackward splitting," Multiscale Model. Simul., vol. 4, pp. 1168-1200, 2005.
51. A. Chambolle, "An algorithm for total variation minimization and applications," Journal of Mathematical Imaging and Vision, vol. 20, no. 1-2, pp. 89-97, 2004, special issue on mathematics and image analysis.
52. R. Courant, "Variational methods for the solution of problems with equilibrium and vibration," Bull. Amer. Math. Soc., vol. 49, pp. 1-23, 1943.
53. Y. Wang, J. Yang, W. Yin, and Y. Zhang, "A new alternating minimization algorithm for total variation image reconstruction," SIAM Journal on Imaging Sciences, vol. 1, no. 3, pp. 248-272, 2008.
54. Z. Botev, J. Grotowski, and D. P. Kroese, "Kernel density estimation via diffusion," Annals of Statistics, vol. 38, pp. 2916-2957, 2010.
55. Z. Botev, 2011, http://www.mathworks.com/matlabcentral/fileexchange/ 17204-kernel-density-estimation.