Comparative Study of the L1 Norm Regression Algorithms

Keywords: L1 norm, Regression, Algorithm, Computer program

Abstract

This paper tries to compare more accurate and efficient L1 norm regression algorithms. Other comparative studies are mentioned, and their conclusions are discussed. Many experiments have been performed to evaluate the comparative efficiency and accuracy of the selected algorithms.


 

References

N.N. Abdelmalek (1980a) L1 solution of overdetermined systems of linear equations. ACM Trans. Math. Soft., 6, 220-227.

N.N. Abdelmalek (1980b) A Fortran subroutine for the L1 solution of overdetermined systems of linear equations. ACM Trans. Math. Soft., 6, 228-30.

D. Anderson, W.L. Steiger (1982) A comparison of methods for discrete L1 curve-fitting. Tech. Rep. DCS-TR-96. Dept. of Comp. Sci., Hill center for the Math. Sci. Busch Campus, New Brunswick, N.J.

R.D. Armstrong, E.L. Frome (1976a) A comparison of two algorithms for absolute deviation curve fitting. JASA, 71, 328-330.

R.D. Armstrong, E.L. Frome, D.S. Kung (1979) A revised simplex algorithm for the absolute deviation curve fitting problem. Commun. Stat. B8, 175-190.

R.D. Armstrong, D.S. Kung (1978) AS132: Least absolute value estimates for a simple linear regression problem. Appl. Stat., 27, 363-366.

Barrodale, F.D.K. Roberts (1973) An improved algorithm for discrete L1 linear approximation. SIAM J. Numer. Anal., 10, 839-848.

Barrodale, F.D.K. Roberts (1974) Algorithm 478: Solution of an overdetermined system of equations in the L1 norm. Commun. ACM, 17, 319-320.

R.H. Bartels, A.R. Conn, J. Sinclair (1978) Minimization technique for piecewise differentiable functions: The L1 solution to an overdetermined linear system. SIAM J. Numer. Anal. 15, 224-241.

Bijan Bidabad (1987a) Least absolute error estimation. The First International Conference on Statistical Data Analysis Based on the L1‎‎ norm and Related Methods, Neuchatel, Switzerland. http://www.bidabad.com/doc/lae-I.pdf

Bijan Bidabad (1987b) Least absolute error estimation, part II. Submitted to the First International Conference on Statistical Data Analysis Based on the L1‎‎ norm and Related Methods, Neuchatel, Switzerland. http://www.bidabad.com/doc/lae-II.pdf

Bijan Bidabad (1988a) A proposed algorithm for least absolute error estimation. Proc. of the Third Seminar of Mathematical Analysis. Shiraz Univ., 24-34, Shiraz, Iran.

Bijan Bidabad (1988b) A proposed algorithm for least absolute error estimation, part II. Proc. of the Third Seminar of Mathematical Analysis, Shiraz Univ., 35-50, Shiraz, Iran.

Bijan Bidabad (1989a) Discrete and continuous L1‎‎ norm regressions, proposition of discrete approximation algorithms and continuous smoothing of concentration surface, Ph.D. thesis, Islamic Azad Univ., Tehran, Iran. http://www.bidabad.com/doc/L1-norm-thesis-en.pdf

Bijan Bidabad (1989b) Discrete and continuous L1‎‎ norm regressions, proposition of discrete approximation algorithms and continuous smoothing of concentration surface, Ph.D. thesis, Islamic Azad Univ., Tehran, Iran. Farsi translation. http://www.bidabad.com/doc/L1-norm-thesis-fa.pdf

Bijan Bidabad (2005). L1 norm based computational algorithms. http://www.bidabad.com/doc/l1-article6.pdf

Bijan Bidabad (2005). L1 norm solution of overdetermined system of linear equations. http://www.bidabad.com/doc/l1-article5.pdf

Bijan Bidabad (2005). L1 norm based data analysis and related methods. http://www.bidabad.com/doc/l1-articl1.pdf

Bijan Bidabad (2005). New algorithms for the L1 norm regression. http://www.bidabad.com/doc/l1-article2.pdf

Bijan Bidabad (2005). Comparative study of the L1 norm regression algorithms. http://www.bidabad.com/doc/l1-articl3.pdf

Bijan Bidabad (2005). Continuous L1 norm estimation of Lorenz curve. http://www.bidabad.com/doc/l1-articl4.pdf

Bijan Bidabad (1993). Estimating Lorenz curve for Iran by using continuous L1 norm estimation, Economics and Management Journal, Islamic Azad University, No. 19, winter 1993, pp. 83-101. http://www.bidabad.com/doc/iraninc-l1.pdf

Bijan Bidabad (2005). Continuous L1 norm estimation of Lorenz curve when probability density function is known.

Bijan Bidabad (2005). USA Income distribution counter-business-cyclical trend (Estimating Lorenz curve using continuous L1 norm estimation). First meeting of the Society for the Study of Economic Inequality (ECINEQ), Palma de Mallorca, Spain, July 20-22, 2005.

http://www.uib.es/congres/ecopub/ecineq/general.html

http://www.uib.es/congres/ecopub/ecineq/papers/039Bidabab.pdf

http://www.bidabad.com/doc/estimating-lorenz-us.pdf

Bijan Bidabad, Hamid Shahrestani. (2008) An implied inequality index using L1 norm estimation of Lorenz curve. Global Conference on Business and Finance Proceedings. Mercedes Jalbert, managing editor, ISSN 1931-0285 CD, ISSN 1941-9589 Online, Volume 3, Number 2, 2008, The Institute for Business and Finance Research, Ramada Plaza Herradura, San Jose, Costa Rica, May 28-31, 2008, pp. 148-163. Global Journal of Business Research, Vol. 4, No. 1, 2010, pp.29-45.

http://www.bidabad.com/doc/L1-Implied-inequality-index-4.pdf

http://www.theibfr.com/archive/ISSN-1941-9589-V3-N2-2008.pdf

http://www.bidabad.com/doc/SSRN-id1631861.pdf

P. Bloomfield, W. Steiger (1980) Least absolute deviations curve fitting. SIAM J. Sci. Statist. Comput. 1, 290-301.

R. Dutter (1977) Numerical solution of robust regression problems, computational aspects, a comparison. J. of Stat. Computation and Simulation, 5, 207-238.

J.E. Gentle, S.C. Narula, V.A. Sposito (1987) Algorithms for unconstrained L1 linear regression. In Y. Dodge (ed.) Statistical data analysis based on the L1 norm and related methods. North-Holland. 83-94.

J.E. Gentle, V.A. Sposito, S.C. Narula (1988) Algorithms for unconstrained L1 simple linear regression. CSDA, 6(4), 335-340.

J. Gilsinn, K. Hoffman, R.H.F. Jackson, E. Leyendecker, P. Saunder, D. Shier (1977) Methodology and analysis for comparing discrete L1 approximation codes., Commun. Stat., B6, 399-413.

K.L. Hoffman, D.R. Shier (1980b) A test problem generator for discrete linear L1 approximation problems. ACM Trans. Math. Soft., 6, 615-617.

L.A. Josvanger, V.A. Sposito (1983) L1-norm estimates for the simple regression problem. Comm. Stat. B12, 215-21.

W.J. Kennedy, J.E. Gentle (1977) Examining rounding error in least absolute values regression computations. Comm. Stat., B6, 415-420.

W.J Kennedy, J.E. Gentle, V.A. Sposito (1977a) Comparisons of algorithms for L1 estimation in the linear model. Paper presented at Midwestern Regional Meeting of IMS, Madison, WI. (Available from the second author).

W.J Kennedy, J.E. Gentle, V.A. Sposito (1977b) A computer oriented method for generating test problems for L1 regression. Comm. Stat., B6, 21-27.

J.L. Larson, A.H. Sameh (1980) Algorithms for round of error analysis a relative error approach. Computing 24, 275-297.

M.J. Mojarrad (1977) The application of comparative Monte Carlo methods to econometrics: an efficient Monte Carlo study of finite sample properties of iterative instrumental variables estimation. Ph.D. Diss., University of Pennsylvania.

A.N. Sadovski (1974) AS74: L1-norm fit of a straight line. Appl. Stat. 23, 244-248.

E.J. Schlossmacher (1973) An iterative technique for absolute deviations curve fitting. JASA 68, 857-865.

E. Seneta, W.L. Steiger (1984) A new LAD curve-fitting algorithm: slightly overdetermined equation system in L1. Discrete Applied Math., 7, 79-91.

G.O. Wesolowsky (1981) A new descent algorithm for least absolute value regression problem. Comm. Stat., B10, 479-491.

Published
2019-06-13
How to Cite
Bidabad, B. (2019). Comparative Study of the L1 Norm Regression Algorithms. Bangladesh Journal of Multidisciplinary Scientific Research, 1(1), 31-40. https://doi.org/10.46281/bjmsr.v1i1.313
Section
Original Articles/Review Articles/Case Reports/Short Communications