A new technique for curve fitting based on minimum absolute deviations

Soliman, S. A.; Christensen, G. S.; Rouhi, Amir H.

doi:10.1016/0167-9473(88)90074-6

Cited by 31 publications

(11 citation statements)

References 14 publications

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“…This development is an improved version of developments by the same authors in [1] and [2]. Essentially, the new method relies on the application of contraction mapping to LAV estimation problems.…”

Section: Discussionmentioning

confidence: 99%

“…, n for the n equations for which the iterative solution, obtained by successive approximations, converges most rapidly. In [1] and [2], the authors first use least squares to determine the measured points having the least error; second, these errors are set to equal zero in order to obtain the LAV estimate for the measured points.…”

Section: Contraction Mapping Theorem [14]mentioning

confidence: 99%

“…In Section IV, solutions obtained by the new method are presented for several examples. In Section V (Conclusions), a comparison is made to results obtained with a method developed in [1]- [6] by the same authors, using material from [7] and [8].…”

Section: Introductionmentioning

confidence: 99%

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A new algorithm for finding the optimal solution of the least absolute value estimation problem

Christensen

Saif

Soliman

2007

Can. J. Electr. Comput. Eng.

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In this paper an algorithm is developed which uses contraction mapping to determine the optimal solution of the least absolute value (LAV) static estimation problem. It is noted that the new algorithm is computationally simpler than other methods currently available for this purpose. Minimal computational effort is required to obtain the LAV estimates.Dans cet article, on présente un algorithme développé qui utilise le traçage contracté pour déterminer la solution optimale du problème d'estimation statique de la moindre valeur absolue (LAV). On note que le nouvel algorithme est logistiquement plus simple que les autres méthodes actuellement disponibles dans ce but. Un minimum d'effort de calculs est requis pour obtenir les estimés de LAV. from 2000 to 2006, and as a Visiting Professor at Sultan Qaboos University, Muscat, during Fall 2006. He earned the first excellent medal and the incentive award as a best scientist in 1992. He has been chosen to be listed in the book Who's Who for the year 2007 for his achievements in his area of expertise. He has authored more than 110 refereed journal papers and more than 70 refereed conference papers. He has co-authored three books in his subject area. His research interests are in power quality, application of fuzzy systems to power systems, and application of state estimation to power systems.

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Section: Discussionmentioning

confidence: 99%

Section: Contraction Mapping Theorem [14]mentioning

confidence: 99%

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A new algorithm for finding the optimal solution of the least absolute value estimation problem

Christensen

Saif

Soliman

2007

Can. J. Electr. Comput. Eng.

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“…Actually they do not attack it directly, but mention it in passing, as having the same problems that they document for the methods of Soliman et al (1988Soliman et al ( , 1991 But if we apply Schlossmacher directly to their counterexamples, no problems occur. Our R code is presented below.…”

Section: Resultsmentioning

confidence: 99%

Simultaneous estimation of quantile curves using quantile sheets

Schnabel

Eilers

2012

AStA Adv Stat Anal

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The results of quantile smoothing often show crossing curves, in particular, for small data sets. We define a surface, called a quantile sheet, on the domain of the independent variable and the probability. Any desired quantile curve is obtained by evaluating the sheet for a fixed probability. This sheet is modeled by P-splines in form of tensor products of B-splines with difference penalties on the array of coefficients. The amount of smoothing is optimized by cross-validation. An application for reference growth curves for children is presented.

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“…In the late 1980s, Christensen, Soliman and Rouhi introduced a technique for curve-fitting based on Least Absolute Value (LAV) minimization technique [11]. The idea was originally developed for power system state estimation.…”

Section: Motivationsmentioning

confidence: 99%