| 1. |
- Arslan, O., et al.
(författare)
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Algorithms to compute CM - and S-estimates for regression
- 2003
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Ingår i: International Conference on Robust Statistics. - : Physica-Verlag Rudolf Liebig GmbH. - 3790815187 ; , s. 62-76
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Konferensbidrag (refereegranskat)abstract
- Constrained M-estimators for regression were introduced by Mendes and Tyler in 1995 as an alternative class of robust regression estimators with high breakdown point and high asymptotic efficiency. To compute the CM-estimate, the global minimum of an objective function with an inequality constraint has to be localized. To find the S-estimate for the same problem, we instead restrict ourselves to the boundary of the feasible region. The algorithm presented for computing CM-estimates can easily be modified to compute S-estimates as well. Testing is carried out with a comparison to the algorithm SURREAL by Ruppert
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| 2. |
- Edlund, Ove
(författare)
-
A software package for sparse orthogonal factorization and updating
- 2002
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Ingår i: ACM Transactions on Mathematical Software. - : Association for Computing Machinery (ACM). - 0098-3500 .- 1557-7295. ; 28:4, s. 448-482
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Tidskriftsartikel (refereegranskat)abstract
- Although there is good software for sparse QR factorization, there is little support for updating and downdating, something that is absolutely essential in some linear programming algorithms, for example. This article describes an implementation of sparse LQ factorization, including block triangularization, approximate minimum degree ordering, symbolic factorization, multifrontal factorization, and updating and downdating. The factor Q is not retained. The updating algorithm expands the nonzero pattern of the factor L, which is reflected in the dynamic representation of L. The block triangularization is used as an `ordering for sparsity' rather than as a prerequisite for block backward substitution. In symbolic factorization, something called `element counters' is introduced to reduce the overestimation of the number of nonzeros that the commonly used methods do. Both the approximate minimum degree ordering and the symbolic factorization are done without explicitly forming the nonzero pattern of the symmetric matrix in the corresponding normal equations. Tests show that the average time used for a single update or downdate is essentially the same as the time used for a single forward or backward substitution. Other parts of the implementation show the same range of performance as existing code, but cannot be replaced because of the special character of the systems that are solved.
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| 3. |
- Edlund, Ove
(författare)
-
CMregr - A Matlab software package for finding CM-Estimates for Regression
- 2004
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Ingår i: Journal of Statistical Software. - : Foundation for Open Access Statistic. - 1548-7660. ; 10:3, s. 1-11
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Tidskriftsartikel (refereegranskat)abstract
- This paper describes how to use the Matlab software package CMregr, and also gives some limited information on the CM-estimation problem itself. For detailed information on the algorithms used in CMregr as well as extensive testings, please refer to Arslan, Edlund & Ekblom (2002) and Edlund & Ekblom (2004).
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