By C. Agostinelli (auth.), Professor Dr. Rudolf Dutter, Professor Dr. Peter Filzmoser, Professor Dr. Ursula Gather, Professor Dr. Peter J. Rousseeuw (eds.)

Aspects of strong records are very important in lots of components. in keeping with the overseas convention on powerful records 2001 (ICORS 2001) in Vorau, Austria, this quantity discusses destiny instructions of the self-discipline, bringing jointly prime scientists, skilled researchers and practitioners, in addition to more youthful researchers. The papers conceal a mess of alternative facets of strong information. for example, the basic challenge of information precis (weights of facts) is taken into account and its robustness homes are studied. additional theoretical matters comprise e.g.: strong equipment for skewness, time sequence, longitudinal information, multivariate equipment, and checks. a few papers take care of computational elements and algorithms. ultimately, the points of program and programming instruments entire the volume.

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In R. Payne, editor, COMPSTAT'98. Proceedings in Computational Statistics. 13th Symposium held in Bristol. England, pages 161-166. Physica, Heidelberg, 1998. D. S. Kung. Min-max estimates for a linear multiple regression problem. Applied Statistics, 28:93-100,1979. D. S. Kung. A dual method for discrete Chebychev curve fitting. Mathematical Programming, 19:186-199, 1980. RD. G. Sklar. A linear programming algorithm for curve fitting in the L oo norm. Numerical Functional Analysis and Optimization, 2:187-218,1980.

These results suggest that for a fixed CPU time, the EAl obtains better approximations to the LMS than the FSA, specially for large data sets. = = 3 Exchange Algorithm for LQD In this section we discuss how to adapt the EA described in Section 2 to the computation of the LQD estimate. The data set of differences {(Xi - Xi' Yi - Yi); 1 ~ i < j ~ n} has size n' = (~). Since each point (Xi - xi) has p - 1 components, the elemental sets and the reference sets are subsets from the DSD of sizes p - 1 and p, respectively.

Many other relevant issues are found in Dodge (1987, 1997) and Dodge and Jureckova (2000). Furthermore, the dual program to (12) is also subject of interest. It consists in maximizing, with respect to Ll i , i = 1, ... ,p and a-I:::; Ll i :::; a, i = 1, ... , n. After the substitution Ll i + (1 - a) = ai == ai(a), i = 1, ... , n, we obtain an equivalent problem to (15), namely, to maximize, with respect to ai, i = 1, ... , n, (16) under the constraints n n LXiiai = (I-a) LXii' j = 1, ... ,n. i=l i=l The optimal solution a = (a1 (a), ...

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