Statistical distances based on Euclidean graphs

Recent Advances in Applied Probability

Volumn , Issue , 2005, Pages 223-239

  Jimenez R ^a   Yukich, J E ^b  

^a UNIVERSIDAD SIMÓN BOLÍVAR   (Venezuela)

^b LEHIGH UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 60649114567     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/0-387-23394-6_10     Document Type: Chapter

References (30)

1. Aldous, D. and J. M. Steele (1992). Asymptotics for Euclidean minimal spanning trees on random points. Probab. Theory Related Fields, 92, 247-258.
2. Aldous, D. and J. M. Steele (2002). The objective method: probabilistic combinatorial optimization and local weak convergence. Encyclopedia of Mathematics, to appear.
3. Aurenhammer, F. (1991). Voronoi diagrams - A survey of a fundamental geometric data structure. ACM Computing Surveys, 23, 3, 345-405.
4. Beardwood, J., Halton, J. H., and J. M. Hammersley (1959). The shortest path through many points. Proc. Camb. Philos. Soc., 55, 299-327.
5. Bickel, P. and L. Breiman (1983). Sums of functions of nearest neighbor distances, moment bounds, limit theorems and a goodness of fit test. Annals of Prob., 11, 185-214.
6. Cheng, R. C. H. and Amin N. A. K. (1983). Estimating parameters in continuous univariate distributions with shifted origin. J. R. Statist. Soc. B, 45, 394-403.
7. Cressie, N and T. R. C. Read (1984). Multinomial goodness-of-fit tests. J. R. Statist. Soc. B, 46, 440-464.
8. Csiszár, I. (1967). Information-type measures of difference of probability distributions and indirect observations Studia Sci. Math. Hungarica, 2, 299-318.
9. th European Meeting of Statist. Academia, Prague, 73-86.
10. Darling, D. A. (1953). On a class of problems related to the random division of an interval. Ann. Math. Statist., 24, 239-253.
11. Dudewicz, E. J. and E. C. Van der Meulen (1987). The empiric entropy, a new approach to nonparametric density estimation. New perspectives in theoretical and applied statistics. Eds. M. I. Puri, J. Vilaplana and M. Wertz. Wiley, New York, 202-227.
12. Dudley, R. M. (1989). Real Analysis and Probability. Wadsworth and Brooks/Cole.
13. Hall, P. (1986). On powerful distributional tests based on sample spacings. J. Multi. Anal. 19, 201-224.
14. Holst, L. (1979). Asymptotic normality of sum-functions of spacings. Annals of Prob., 7, 1066-1072.
15. Holst, L. and J. S. Rao (1981). Asymptotic spacings theory with applications to the two-sample problem. Canadian J. Statist., 9, 79-89.
16. Jiménez, R. and Y. Shao (2001). On robustness and efficiency of minimum divergence estima-ators, Test, 10, 2, 241-248.
17. Jiménez, R. and J. E. Yukich (2002). Asymptotics for statistical distances based on Voronoi tessellations, Journal of Theoretical Probability, 15, 2, 503-541.
18. Jimenez, R. and J. E. Yukich (2002). Strong laws for Euclidean graphs with general edge weights, Statist. Probab. Lett., 56, 251-259.
19. Lindsay, B. G. (1994). Efficiency versus robustness: the case for minimum Hellinger distance and related methods. Annals of Statistics, 22, 1081-1114.
20. McGivney, K. and J. E. Yukich (1999). Asymptotics for Voronoi tessellations on random samples. Stochastic Process. Appl., 83, 273-288.
21. Möller, J. (1994). Lectures on Random Voronoi Tessellations. Lecture Notes in Statistics, 87, Springer-Verlag.
22. Okabe, A., Boots, B., and K. Sugihara (1992). Spatial Tessellations - Concepts and Applications of Voronoi Diagrams. J. Wiley and Sons, England.
23. Penrose, M. D. and J. E. Yukich (2001). Central limit theorems for some graphs in computational geometry. Ann. Appl. Probab. 11, 1005-1041.
24. Penrose, M. D. and J. E. Yukich (2002). Weak laws of large numbers in geometric probability. Ann. Appl. Probab., to appear.
25. Pyke, R. (1965). Spacings. Royal Statist. Soc. B, 27, 395-436.
26. Ranneby, B. (1984). The maximum spacing method. An estimation method related to the maximum likelihood method. Scand. J. Statist., 11, 93-112.
27. Shao, Y. and M. G. Hahn (1995). Limit theorems for logarithm of sample spacings. Statistics and Probability Letters, 24, 121-132.
28. Shao, Y. and M. G. Hahn (1999). Strong consistency of the maximum product of spacings estimates with applications in nonparametrics and in estimation of unimodal densities. Ann. Inst. Statist., 51, Math. 31-49.
29. Steele, J. M. (1997). Probability Theory and Combinatorial Optimization. SIAM.
30. Yukich, J. E. (1998). Probability Theory of Classical Euclidean Optimization Problems. Lecture Notes in Mathematics, 1675, Springer, Berlin.