On the least median square problem

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2004, Pages 273-279

  Erickson, Jeff ^a   Har Peled, Sariel ^a   Mount, David M ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b University of Maryland ^*  (United States)

Author keywords

Approximation algorithms; LMS regression; Lower bounds; Robust statistics

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; MATHEMATICAL TRANSFORMATIONS; PROBABILITY; PROBLEM SOLVING; REGRESSION ANALYSIS; STATISTICAL METHODS;

APROXIMATION ALGORITHMS; LEAST MEDIAN-OF-SQUARES (LMS) REGRESSION; LOWER BOUNDS; ROBUST STATISTICS;

COMPUTATIONAL COMPLEXITY;

EID: 4544357050     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/997817.997859     Document Type: Conference Paper

References (26)

1. J. Basch, L. J. Guibas, and J. Hershberger. Data structures for mobile data. Proc. 8th ACM-SIAM Sympos. Discrete Algorithms, 747-756, 1997
2. M. Ben-Or. Lower bounds for algebraic computation trees. Proc. 15th Annu. ACM Sympos. Theory Comput., 80-86, 1983.
3. T. M. Chan. Geometric applications of a randomized optimization technique. Discrete Comput. Geom. 22:547-567, 1999.
4. T. M. Chan. Low-dimensional linear programming with violations. Proc. 43th Annu. IEEE Sympos. Found. Comput. Sci., 570-579, 2002.
5. T. M. Chan. Personal communication, Feb. 2004.
6. B. Chazelle. The Discrepancy Method. Cambridge University Press, 2000.
7. H. Edelsbrunner and D. L. Souvaine. Computing median-of-squares regression lines and guided topological sweep. J. Amer. Statist. Assoc. 85:115-119, 1990.
8. I. Emiris and J. Canny. A general approach to removing degeneracies. SIAM J. Comput. 24:650-664, 1995.
9. I. Z. Emiris, J. F. Canny, and R. Seidel. Efficient perturbations for handling geometric degeneracies. Algorithmica 19(1-2):219-242, 1997.
10. J. Erickson. On the relative complexities of some geometric problems. Proc. 7th Canad. Conf. Comput. Geom., 85-90, 1995.
11. J. Erickson. Lower bounds for linear satisfiability problems. Chicago J. Comput. Sci. 1999(8), 1999.
12. J. Erickson. New lower bounds for convex hull problems in odd dimensions. SIAM J. Comput. 28:1198-1214, 1999.
13. J. Erickson and R. Seidel. Better lower bounds on detecting affine and spherical degeneracies. Discrete Comput. Geom. 13:41-57, 1995.
14. 2) problems in computational geometry. Comput. Geom. Theory Appl. 5:165-185, 1995.
15. S. Har-Peled. On core-sets and slabs. Manuscript, 2003.
16. S. Har-Peled and Y. Wang. Shape fitting with outliers. Proc. 19th Annu. ACM Sympos. Comput. Geom., 29-38, 2002.
17. L. Khachiyan. On the complexity of approximating determinants in matrices. J. Complexity 11:138-153, 1995.
18. J. Matoušek. On geometric optimization with few violated constraints. Discrete Comput. Geom. 14:365-384, 1995.
19. P. Meer, D. Mintz, A. Rosenfeld, and D. Y. Kim. Robust regression methods for computer vision: A review. Int. J. Computer Vision 6:59-70, 1991.
20. D. M. Mount, N. S. Netanyahu, K. R. Romanik, R. Silverman, and A. Y. Yu. A practical approximation algorithm for the LMS line estimator. Proc. 8th ACM-SIAM Sympos. Discrete Algorithms, 473-482, 1997.
21. C. F. Olson. An approximation algorithm for least median of squares regression. Inform. Process. Lett. 63:237-241, 1997.
22. P. J. Rousseeuw. Least median of squares regression. J. Amer. Statist. Assoc. 79(388):871-880, 1984.
23. P. J. Rousseeuw. Introduction to positive breakdown methods. Handbook of Statistics, Vol. 15: Robust Inference, 101-121, 1997. Elsevier.
24. P. J. Rousseeuw and A. M. Leroy. Robust Regression and Outlier Detection. John Wiley & Sons, New York, 1987.
25. A. C. Yao. Lower bounds for algebraic computation trees with integer inputs. SIAM J. Comput. 20(4):655-668, 1991.
26. V. J. Yohai. High breakdown-point and high efficiency robust estimates for regression. Ann. Stat. 15:642-656, 1987.