Optimal parametric density estimation by minimizing an analytic distance measure

FUSION 2007 - 2007 10th International Conference on Information Fusion

Volumn , Issue , 2007, Pages

  Hanselmann, Anne ^a   Schrempf, Oliver C ^a   Hanebeck, Uwe D ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Density estimation; Dirac mixture densities; Distance measure; Gaussian mixture densities

Indexed keywords

DATA FUSION; DISTRIBUTION FUNCTIONS; ESTIMATION; FUSION REACTIONS; INFORMATION FUSION; INTEGRAL EQUATIONS; MAXIMUM LIKELIHOOD ESTIMATION; NUCLEAR PHYSICS; OPTIMIZATION; RESPONSE TIME (COMPUTER SYSTEMS); SENSOR DATA FUSION; SOUND REPRODUCTION;

ANALYTIC OPTIMIZATION; APPROXIMATION FUNCTIONS; CUMULATIVE DISTRIBUTION FUNCTION; DENSITY ESTIMATION; DENSITY FUNCTIONS; DIRAC MIXTURE DENSITIES; DISTANCE MEASURE; DISTANCE MEASURES; GAUSSIAN MIXTURE DENSITIES; INTERNATIONAL CONFERENCES; MAXIMUM-LIKELIHOOD; MINIMIZATION PROBLEMS;

PARAMETER ESTIMATION;

EID: 50149118621     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICIF.2007.4408100     Document Type: Conference Paper

References (14)

1. V. Peterka, "Bayesian System Identification," Automatica, vol. 17, no. 1, pp. 41-53, Jan. 1981.
2. M. Ramoni and P. Sebastiani, "Parameter Estimation in Bayesian Networks from Incomplete Databases." Intell. Data Anal., vol. 2, no. 1-4, pp. 139-160, 1998.
3. D. Freedman and P. Diaconis, "On the Histogram as a Density Estimator: L2 Theory," Probability Theory and Related Fields, vol. V57, no. 4, pp. 453-476, Dec. 1981.
4. E. Parzen, "On Estimation of a Probability Density Function and Mode," The Annals of Mathematical Statistics, vol. 33, no. 3, pp. 1065-1076, Sep. 1962.
5. J. Aldrich, "R. A. Fisher and the Making of Maximum Likelihood 1912-1922," Statistical Science, vol. 12, no. 3, pp. 162-176, aug 1997.
6. Dempster, A. P., Laird, N. M., and Rubin, D. B., "Maximum Likelihood from Incomplete Data via the EM Algorithm," Journal of the Royal Statistical Society. Series B (Methodological), vol. 39, no. 1, pp. 1-38, 1977.
7. O. C. Schrempf, D. Brunn, and U. D. Hanebeck, "Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering," in Proceedings of the 45th IEEE Conference on Decision and Control (CDC'06), San Diego, California, USA, Dec. 2006.
8. _, "Dirac Mixture Density Approximation Based on Minimization of the Weighted Cramér-von Mises Distance," in Proceedings of the International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006), Heidelberg, Germany, Sep. 2006, pp. 512-517.
9. M. D. Weber, L. M. Leemis, and R. K. Kincaid, "Minimum Kolmogorov-Smirnov Test Statistic Parameter Estimates," Journal of Statistical Computation and Simulation, vol. 76, no. 3, pp. 196-206, 2006.
10. K. Pearson, "On the Systematic Fitting of Curves to Observations and Measurements," Biometrika, vol. 1, no. 3, pp. 265-303, Apr. 1902.
11. D. M. Titterington, A. F. M. Smith, and U. E. Makov, Statistical Analysis of Finite Mixture Distributions, ser. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, 1985.
12. R. B. D'Agostino and M. A. Stephens, Eds., Goodness-of-Fit Techniques, ser. Statistics, textbooks and monographs. Marcel Dekker, Inc., 1986, vol. 68.
13. S. P. Lloyd, "Least Squares Quantization in PCM," IEEE Transactions on Information Theory, vol. IT-28, no. 2, pp. 129-137, Mar. 1982.
14. U. D. Hanebeck, K. Briechle, and A. Rauh, "Progressive Bayes: A New Framework for Nonlinear State Estimation," in Proceedings of SPIE, vol. 5099, Orlando, Florida, 2003, pp. 256-267, AeroSense Symposium.