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Solve least absolute value regression problems using modified goal programming techniques. (English) Zbl 1042.90612


MSC:

90C29 Multi-objective and goal programming
62J99 Linear inference, regression

Software:

Mathematica; LINDO; alr3
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Full Text: DOI

References:

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[3] Dielman, T.E., Computational algorithms for least absolute value regression. In \(L_1\); Dielman, T.E., Computational algorithms for least absolute value regression. In \(L_1\)
[4] Armstrong, R. D.; Frame, E. L.; Kung, D. S., A revised simplex algorithm for the absolute deviation curve fitting problem, Commun. Statist. Simul. Comput. B, 8, 175-190 (1979) · Zbl 0439.65049
[5] Abdelmalek, N. N., A FORTRAN subroutine for the \(L_1\) solution of overdetermined systems of linear equations, ACM Trans. Math. Software, 6, 228-230 (1980)
[6] Bloomfield, P.; Steiger, W., Least absolute deviations curve: Fitting, SIAM J. Sci. Statist. Comput., 1, 290-300 (1980) · Zbl 0471.65007
[7] Ignizio, J., Introduction to Linear Goal Programming; Ignizio, J., Introduction to Linear Goal Programming · Zbl 0662.90075
[8] Armstrong, R. D.; Kung, M. T., A dual algorithm to solve linear least absolute value problems, J. Oper. Res. Soc., 33, 931-936 (1982) · Zbl 0489.90065
[9] Gentle, J. E., Narula, S. C., and Sposito, V. A., Testing software for robust regression. In \(L_1\); Gentle, J. E., Narula, S. C., and Sposito, V. A., Testing software for robust regression. In \(L_1\)
[10] Bazaraa, M. S., Jarvis, J. J. and Sherali, H. D., Linear Programming and Network Flows; Bazaraa, M. S., Jarvis, J. J. and Sherali, H. D., Linear Programming and Network Flows · Zbl 0722.90042
[11] Winston, W., Operations Research: Applications and Algorithms; Winston, W., Operations Research: Applications and Algorithms · Zbl 0672.90082
[12] Gonin, R. and Money, A. H., Nonlinear LP-Norm Estimation; Gonin, R. and Money, A. H., Nonlinear LP-Norm Estimation
[13] Schrage, L., LINDO: User’s Manual; Schrage, L., LINDO: User’s Manual
[14] Li, H. L., Technical note: An efficient method for solving linear goal programming problems, J. Opt. Theory Appl., 90, 465-469 (1996) · Zbl 0866.90112
[15] Taylor, M. S.; Thompson, J. R., Database random number generation for a multivariate distribution via stochastic simulation, Comput. Statist. Data Anal., 4, 93-101 (1986)
[16] Weisberg, S., Applied Linear Regression; Weisberg, S., Applied Linear Regression · Zbl 0529.62054
[17] Gunst, R. F. and Mason, R. L., Regression Analysis And Its Application: A Data-Oriented Approach; Gunst, R. F. and Mason, R. L., Regression Analysis And Its Application: A Data-Oriented Approach · Zbl 0433.62041
[18] Mathematica User’s Guide for Microsoft Windows; Mathematica User’s Guide for Microsoft Windows
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