By C. Agostinelli (auth.), Professor Dr. Rudolf Dutter, Professor Dr. Peter Filzmoser, Professor Dr. Ursula Gather, Professor Dr. Peter J. Rousseeuw (eds.)
Aspects of sturdy records are vital in lots of components. in accordance with the foreign convention on powerful facts 2001 (ICORS 2001) in Vorau, Austria, this quantity discusses destiny instructions of the self-discipline, bringing jointly top scientists, skilled researchers and practitioners, in addition to more youthful researchers. The papers conceal a large number of alternative elements of strong statistics. for example, the basic challenge of knowledge precis (weights of facts) is taken into account and its robustness houses are studied. additional theoretical matters contain e.g.: powerful equipment for skewness, time sequence, longitudinal facts, multivariate tools, and exams. a few papers take care of computational points and algorithms. ultimately, the features of program and programming instruments entire the volume.
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Additional resources for Developments in Robust Statistics: International Conference on Robust Statistics 2001
A. Mirzaian and E. Arjomandi. Selection in X + Y and matrices with sorted rows and columns. Information Processing Letters, 20:13-17,1985. J. Rousseeuw. Least median of squares regression. J. Am. Statist. , 79:871-880, 1984. J. M. Leroy. Robust regression and outlier detection. Wiley, New York, 1987. E. Stiefel. Uber diskrete und lineare Tschebyscheff Approximationen. Numerische Mathematik, 1:1-28, 1959. E. Stiefel. Note on Jordan elimination, linear programming and Tschebyscheff approximation.
The exact LQS estimate coincides with the Chebyshev fit of the reference set yielding the smallest hth absolute residual. Agu1l6 (1997) introduced some speed-ups in Stromberg's algorithm and proposed a branch-and-bound algorithm for computing the LQS estimate. In Croux et al. (1994) it is noticed that the exact LQD estimate can be computed examining the Chebychev fits of all p-subsets from the DSD. The branch-and-bound algorithm of Agu1l6 (1997) can be also adapted for computing the exact LQD estimate.
The procedure is repeated many times, each time starting from a random reference set. Finally, the feasible solution with the smallest Chebyshev criterion found by the FSA is returned as an approximation of the LMS estimate. A straightforward method for computing the LQD starts by computing and storing the (~) observations of the DSD and then applying the FSA to the DSD. Since this method stores the (~) observations ofthe DSD, it needs O(n 2 ) space. Moreover, each exchange needs O(n 2 ) time since the computation of (~) residuals is required.
Developments in Robust Statistics: International Conference on Robust Statistics 2001 by C. Agostinelli (auth.), Professor Dr. Rudolf Dutter, Professor Dr. Peter Filzmoser, Professor Dr. Ursula Gather, Professor Dr. Peter J. Rousseeuw (eds.)