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Linear programming approach to LMS-estimation. (English) Zbl 0875.62292
Summary: In the paper a probabilistic algorithm, based on the Simplex Method, is suggested for minimization of the k-th smallest value of absolute residuals in linear regression. In particular it is suitable for computation of the Least Median of Squares (LMS) estimator of P.J. Rousseeuw, A.M. Leroy [4]. Numerical results indicate that the algorithm represents an improvement in comparison with those put forward earlier.

MSC:
62J05 Linear regression; mixed models
90C90 Applications of mathematical programming
65C99 Probabilistic methods, stochastic differential equations
90C05 Linear programming
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References:
[1] Arthanari, T. S.; Dodge, Y.: Mathematical programming in statistics. (1981) · Zbl 0549.62002
[2] Draper, N. R.; Smith, H.: Applied regression analysis. (1966) · Zbl 0158.17101
[3] Hadley, G.: Linear programming. (1962) · Zbl 0102.36304
[4] Leroy, A. M.; Rousseeuw, P. J.: Robust regression and outlier detection. (1987) · Zbl 0711.62030
[5] Tichavský, P.: Algorithms for and geometrical characterizations of solutions in the LMS and LTS linear regression. 139-151 (1981)
[6] Víšek, J. Á.: What is adaptivity of regression analysis intended for?. Transactions of ROBUST’90, 160-181 (1990)
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