111
Views
58
CrossRef citations to date
0
Altmetric
Original Articles

Least absolute values estimation: an introduction

Pages 313-328 | Published online: 27 Jun 2007

References

  • Abdelmalek , N. N. 1971 . Linear L1, approximation for a discrete point set and L1, solutions of overdetermined linear equations . J. Assoc. Comput. Mach. , 18 : 41 – 47 .
  • Abdelmalek , N. N. 1974 . On the discrete linear L1. approximation and L1, solutions of overdetermined equations . J. Approx. Theory , 11 : 38 – 53 .
  • Abdelmalek , N. N. 1975 . An efficient method for the discrete linear L1 approximation problem . Math. Comput. , 29 : 844 – 850 .
  • Abdelmalek, N. N. (1976). L1 solution of overdetermined system of linear equations by a dual simplex method and LU decomposition. Tech. Report, Div. of Elec. Eng., Nat’1. Res. Council, Ottawa.
  • Anderson , D. W. 1965 . Linear programming time estimating equations . J. Indust. Eng. , 16 : 136 – 138 .
  • Appa , G. and Smith , C. 1973 . On L1 and Chebyshev estimation . Math. Programming , 5 : 73 – 87 .
  • Armstrong , R. D. , Elam , J. J. and Hultz , J. W. 1977 . Obtaining least absolute value estimates for a two-way classification model . Commun. Statist. B , 6 (This issue)
  • Armstrong , R. D. and Frame , E. L. 1976a . A comparison of two algorithms for absolute deviation curve fitting . J. Amer. Statist. Assoc. , 71 : 328 – 330 .
  • Armstrong , R. D. and Frome , E. L. 1976b . Proceedings of the Statistical Computing Section . The calculation of least absolute value estimators for two-way tables . 1976b . pp. 101 – 106 . Washington, D. C : American Statistical Association .
  • Armstrong, R. D. & Frame, E. L. (1976c). A revised simplex algorithm for the absolute deviation curve fitting problem. Tech. Report, Dept. of General Business, Univ. of Texas, Austin, Texas.
  • Armstrong, R. D. & Frome, E. L. (1976d). Least absolute value estimators for one-way and two-way tables. Tech. Report CCS266, Center for Cybernetic Studies, Univ. of Texas, Austin, Texas.
  • Armstrong , R. D and Frome , E. 1977 . A special purpose linear programming algorithm for obtaining least absolute value estimates in a linear model with dummy variables . Commun. Statist. B , 6 (This issue)
  • Armstrong , R. D and Hultz , J. W. 1977 . An algorithm for a restricted discrete approximation problem in the L1, norm . SIAM J. Numer. Anal. , 14 : 555 – 365 .
  • Ashar , V. G. and Wallace , T. D. 1963 . A sampling study of minimum absolute deviations estimators . Operat. Res. , 11 : 747 – 758 .
  • Barrodale , I. 1968 . L1 approximation and the analysis of data . Appl. Statist. , 17 : 51 – 57 .
  • Barrodale , I. 1970 . “ On computing best L1 approximations ” . In Approximation Theory , Edited by: Talbot , A. 205 – 215 . New York : Academic Press .
  • Barrodale , I. and Roberts , F. D. K. 1970 . “ Applications of mathematical programming to ℓp approximation ” . In Nonlinear Programming , Edited by: Rosen , J. B. , Mangasarian , O. L. and Ritter , K. 447 – 464 . New York : Academic Press .
  • Barrodale, I. Roberts, F. D. K. (1972). An improved algorithm for discrete L1 linear approximation. Tech. Report TSR 1172, Math. Research Center, Univ. of Wisconsin, Madison, Wisconsin.
  • Barrodale , I. and Roberts , F. D. K. 1973 . An improved algorithm for discrete L1linear approximation . SIAM J. Numer. Anal. , 10 : 839 – 848 .
  • Barrodale , I. and Roberts , F. D. K. 1974 . Algorithm 478: Solution of an overdetermined system of equations in the ℓ1 norm . Commun. Assoc. Comput. Mach. , 17 : 319 – 320 .
  • Barrodale , I. and Roberts , F. D. K. 1977a . An efficient algorithm for discrete ℓ1, linear approximation with linear constraints . SIAM J. Numer. Anal. , To appear
  • Barrodale, I. & Roberts, F. D. K. (1977b). Solution of the constrained ℓ1 linear approximation problem. Tech. Report DM-104-IR, Math. Dept., Univ. of Victoria, Victoria, British Columbia.
  • Barrodale , I. and Roberts , F. D. K. 1977c . Algorithms for restricted LAV estimation . Commun. Statist. B , 6 (This issue)
  • Barrodale , I. , Roberts , F. D. K. and Hunt , C. R. 1970 . Computing best ℓp approximations by functions nonlinear in one parameter . Computer J. , 13 : 382 – 386 .
  • Barrodale , I. and Young , A. 1966 . Algorithms for best L1 and L∞ linear approximations on a discrete set . Numer. Math. , 8 : 295 – 306 .
  • Bartels , R. 1976 . Proceedings of the Ninth Interface Symposium on Computer Science and Statistics . Least squares regression as a subtask in more general types of regression . 1976 . pp. 152 – 157 . Boston, Prindle : Weber & Schmidt, Inc. . (D. C. Hoaglin & R. E. Welsch, Eds.)
  • Bartels , R. H. and Conn , A. R. 1997a . Linearly constrained discrete L1 problems . Assoc. Comput. Mach. Trans. Math. Software , To appear
  • Bartels , R. H. and Conn , A. R. 1977b . LAV regression: A special case of piecewise linear minimization . Commun. Statist. B , 6 (This issue)
  • Bartels, R. H., Conn, A. R. & Sinclair, J. W. (1976). A FORTRAN program for solving over determined systems of linear equations in the L1 sense. Tech. Report 236, Dept. of Math. Sci., The John Hopkins Univ. Baltimore, Maryland.
  • Bartels , R. H. , Conn , A. R. and Sinclair , J. W. 1977 . Minimization techniques for piecewise differentiable functions: The L1 solution to an overdetermined linear system . SIAM J. Numer. Anal. , To appear
  • Bassett, G. W. (1973). Some Properties of the Least Absolute Error Estimator. Unpublished Ph.D. thesis, Dept. of Econ. Univ. of Michigan, Ann Arbor, Michigan.
  • Basset , G. W. and Koenker , R. 1977 . Regression quantiles . Econometrica , To appear
  • Bejar , J. 1956 . Regressión en mediana y la programación lineal. (English summary.) . Trab. Estadist. , 7 : 141 – 158 .
  • Bejar , J. 1957 . Cálculo práctico de la regresion en mediana. (English summary) . Trab. Estadist. , 8 : 157 – 173 .
  • Ben-Israel , A. and Charnes , A. 1968 . An explicit solution of a special class of linear programming problems . Operat. Res. , 16 : 1166 – 1175 .
  • Berztiss , A. T. 1964 . Least Squares fitting of polynomials to irregularly spaced data . SIAM Rev. , 6 : 203 – 227 .
  • Blattberg , R. and Sargent , T. 1971 . Regression with non-gaussian stable disturbances: Some sampling results . Econometrica , 39 : 501 – 510 .
  • Boscovich , R. J. 1757 . De litteraria expeditione per pontificiam ditionem, et synopsis amplioris operis, ac habentur plura ejus ex exemplaria etiam sensorum impressa . Bononiesi Scientiarum et Artum Instituto atque Academia Commentarii , 4 : 353 – 396 .
  • Bourdon, G. A. (1974). A Monte Carlo sampling study for further testing of the robust regression procedure based upon the kurtosis of the least squares residuals. Unpublished M. S. thesis. Air Force Institute of Technology, Wright-Patterson AFB, Ohio.
  • Bruen , C. 1938 . Methods for the combination of observations: modal point or most lesser-deviations, median loci or least deviations, mean loci or least squares, and midpoint of least range or least greatest-deviation . Metron , 13 : 6l – 140 .
  • Charnes , A. and Cooper , W. W. 1964 . “ Absolute deviations and constrained regressions ” . In ONR Research Memorandum 96 , Pittsburg, Pennsylvania : Carnegie-Mellon Univ. .
  • Charnes , A. , Cooper , W. W. and Ferguson , R. O. 1955 . Optimal estimation of executive compensation by linear programming . Management Sci. , 1 : 138 – 150 .
  • Cheney, E. W. (1974). A bibliography for approximation theory 1970-1974. Tech. Report CNA-94, Center for Numerical Analysis, Univ. of Texas, Austin, Texas.
  • Claerbout , J. F. and Muir , F. 1973 . Robust modeling with erratic data . Geophysics , 38 : 826 – 844 .
  • Crocker , D. C. 1969 . Linear programming techniques in regression analysis: The hidden danger . AIEE Trans. , 1 : 112 – 126 .
  • Davies , M. 1967 . Linear approximation using the criterion of least total deviations . J. R. Statist. Soc. B , 29 : 101 – 109 .
  • Draper , N. R. and Smith , H. 1966 . Applied Regression Analysis , New York : John Wiley & Sons, Inc. .
  • Dufton , A. F. 1928 . Correlation . Nature , 121 : 866 – 866 .
  • Duris , C. S. and Sreedharan , V. P. 1968 . Chebyshev and ℓ1 solutions of linear equations using least squares solutions . SIAM J. Numer. Anal. , 5 : 491 – 505 .
  • Edgeworth , F. Y. 1887 . On observations relating to several quantities . Phil. Mag. (5th Ser.) , 24 : 222 – 223 .
  • Edgeworth , F. Y. 1888 . On a new method of reducing observations relating to several quantities . Phil. Mag. (5th Ser.) , 25 : 184 – 191 .
  • Eisenhart , C. 1961 . “ Boscovich and the combination of observations ” . In Roger Joseph Boscovich, S. J., F. R. S., 1711-1787: Studies of his Life and Work on the 250th Anniversary of his Birth , Edited by: White , L. L. 200 – 212 . London : Allen and Unwin, Ltd. .
  • Eisenhart , C. 1962 . Actes du Symposium International R. J. Boskovic 1961 . Roger Joseph Boscovich and the combination of observations . 1962 . pp. 19 – 25 . Beogard-Zagreb-Ljubljana
  • Eisenhart , C. 1964 . The meaning of “least” in least squares . J. Washington Acad. Sci. , 54 24 – 33 .
  • Ekblom , H. 1973 . A note on nonlinear median estimators . J. Amer. Statist. Assoc. , 68 431 – 432 .
  • Ekblom , H. 1974 . Lp-methods for robust regression . BIT , 14 22 – 32 .
  • Ekblom , H. and Henriksson , S. 1969 . Lp-criteria for the estimation of location parameters . SIAM J. Appl. Math. , 17 1130 – 1141 .
  • Fair , R. C. 1974 . On the robust estimation of econometric models . Ann. Econ. Soc. Measurement , 3 667 – 677 .
  • Fisher , R. A. 1934 . Two new properties of mathematical likelihood . Proc. R. Soc. A , 144 285 – 307 .
  • Fisher , W. D. 1961 . A note on curve fitting with minimun deviations by linear programming . J. Amer. Statist. Assoc. , 56 359 – 362 .
  • Forsythe , A. B. 1972 . Robust estimation of straight line regression coefficients by minimizing pth power deviations . Technometrics , 14 159 – 166 .
  • Forth, C. R. (1974). Robust estimation techniques for population parameters and regression coefficients. Unpublished M. S. thesis. Air Force Institute of Technology, Wright-Patterson AFB, Ohio.
  • Frome , E. L. and Armstrong , R. D. 1977 . Proceedings of the Tenth Symposium on the Interface . A robust procedure for estimating the trend-cycle component of an economic time series . 1977 . Gaithersburg : National Bureau of Standards . D. Hogben, Ed.
  • Frame, E. L. & Yakatan, G. J. (1976). Statistical estimation of the pharmacokinetic parameters in the one compartment open model. Tech. Report CCS 269, Center for Cybernetic Studies, Univ. of Texas, Austin, Texas.
  • Gallant , A. R. and Gerig , T. M. 1974 . Comments on computing minimum absolute deviations regressions by iterative least squares regressions and by linear programming , No. 911 Raleigh, North Carolina : Institute of Statistics, North Carolina State Univ. . Mimeo
  • Gentle , J. E. , Kennedy , W. J. and Sposito , V. A. 1976 . “ Properties of the L1-estimate space ” . In Proceedings of the Statistical Computing Section , 163 – 164 . Washington, D. C : American Statistical Association .
  • Gentle , J. E. , Kennedy , W. J. and Sposito , V. A. 1977a . On least absolute deviations estimations . Commun. Statist. A , 6 : 839 – 845 .
  • Gentle , J. E. , Kennedy , W. J. and Sposito , V. A. 1977b . On properties of L1 estimators . Math. Programming , 12 : 139 – 140 .
  • Gentle , J. E. and Hanson , T. A. 1977 . Proceedings of the Statistical Computing Section . Variable selection under L1 . 1977 . Washington, D. C : American Statistical Association .
  • Gilsinn , J. , Hoffman , K. , Jackson , R. H. F. , Leyendecker , E. , Saunders , P. and Shier , D. 1977 . Methodology and analysis for comparing discrete linear L1 approximation codes . Commun. Statist. B , 6 This issue
  • Glahe , F.R. and Hunt , J. G. 1970 . The small sample properties of simultaneous equation least absolute estimators vis-a-vis least squares estimators . Econometrica , 38 : 742 – 753 .
  • Hanson, T. A. (1977). Algorithm for best subset selection under L1. Tech. Report, Stat. Lab., Iowa State Univ., Ames, Iowa.
  • Harris , T. E. 1950 . Regression using minimum absolute deviations . Amer. Statistician , 4 : 14 – 15 .
  • Harter , H. L. l974a . The method of least squares and some alternatives I . Int. Statist. Rev. , 42 : l47 – 174 .
  • Harter , H. L. 1974b . The method of least squares and some alternatives II . Int. Statist. Rev. , 42 : 235 – 264 .
  • Harter , H. L. 1975a . The method of least squares and some alternatives III . Int. Statist. Rev. , 43 : 1 – 44 .
  • Harter , H. L. 1975b . The method of least squares and some alternatives IV . Int. Statist. Rev. , 43 : 125 – 190 . 273-8
  • Harter , H. L. 1975c . The method of least squares and some alternatives V . Int. Statist. Rev. , 43 : 269 – 272 .
  • Harter , H. L. 1976 . The method of least squares and some alternatives VI . Int. Statist. Rev. , 44 : 113 – 159 .
  • Harter , H. L. 1977 . Nonuniqueness of least absolute values regression . Comm. Statist. A , 6 : 829 – 838 .
  • Harvey , A. C. 1977 . A comparison of preliminary estimators for robust regression . J. Amer. Statist. Assoc. , 72 : 910 – 913 .
  • Hill , R. W. and Holland , P. W. 1977 . Two robust alternatives to least-squares regression . J. Amer. Statist. Assoc. , 72 : 828 – 833 .
  • Hoel , P. G. 1935 . Certain problems in the theory of closest approximation . Amer. J. Math. , 57 : 891 – 901 .
  • Hogg , R. V. 1974 . Adaptive robust procedures: A partial review and some suggestions for future applications and theory . J. Amer. Statist. Assoc. , 69 : 909 – 923 .
  • Housner , G. W. and Brennan , J. F. l948 . The estimation of linear trends . Ann. Math. Statist. , 19 : 380 – 388 .
  • Huber , P. J. and Dutter , R. . COMPSTAT 1974, Proceedings in Computational Statistics . Numerical solution of robust regression problems . 1974 . pp. 165 – 172 . Vienna : Physica Verlag . (Bruckmann, Ferschl & Schmetterer, Eds.)
  • Jackson , D. 1921 . Note on the median of a set of numbers . Bull. Amer. Math. Soc. , 27 : l60 – 164 .
  • Karst , O. J. 1958 . Linear curve fitting using least deviations . J. Amer. Statist. Assoc. , 53 : 118 – 132 .
  • Kelley , J. E. 1958 . An application of linear programming to curve fitting . SIAM J. Appl. Math. , 6 : 15 – 22 .
  • Kennedy , W. J. and Gentle , J. E. 1977 . Examining rounding error in LAV regression computations . Commun. Statist. B , 6 (This issue)
  • Kennedy, W. J., Gentle, J. E. & Sposito, V. A. (1977a). Comparison of algorithms for L1. estimation in the linear model. Tech. Report, Stat. Lab., Iowa State Univ., Ames, Iowa.
  • Kennedy , W. J. , Gentle , J. E. and Sposito , V. A. 1977b . A computer oriented method for generating test problems for L1 regression . Comm. Statist. B , 6 : 21 – 27 .
  • Kiountouzis , E. A. 1971 . Optimal Lp approximation technqiues and data analysis . Bull. Soc. Math. Greece , 12 : 191 – 206 .
  • Kiountouzis , E. A. 1973 . Linear programming techniques in regression analysis . Appl. Statist. , 22 : 69 – 73 .
  • Koenker, R. & Bassett, G. W. (1976). The asymptotic distribution of the least absolute error estimator. Tech. Report, Dept. of Econ., Univ. of Illinois at Chicago-Circle, Chicago, Illinois.
  • Kripke , B. R. and Rivlin , T. J. 1965 . Approximation in the metric of L1 (X, u) . Trans. Amer. Math. Soc. , 119 : 101 – 122 .
  • Laplace, P. S. (1793). Sur quelques points du systems du monde. Memoires de l’Academic Royale des Sciences de Paris Annee 1789, 1-87. Reprinted in Oeuvres Completes de Laplace, Vol. II. Paris: Gauthier-Villars (1895), 477-558.
  • Marsaglia , G. 1970 . “ One-sided approximations by linear combinations of functions ” . In Approximation Theory , Edited by: Talbot , A. 233 – 242 . New York : Academic Press .
  • Mc Cormick , G. F. and Sposito , V. A. 1975 . A note on L1 estimation based on the median positive quotient . Appl. Statist. , 24 : 347 – 350 .
  • Mc Cormick , G. F. and Sposito , V. A. 1976 . Using the L2-estimator in L1-estimation . SIAM J. Numer. Anal. , 13 : 337 – 343 .
  • Meyer , J. R. and Glauber , R. R. 1964 . “ Division of Research memoir ” . In Investment Decisions, Economic Forecasting and Public Policy , Cambridge, Massachuetts : Grad. School Bus. Ad., Harvard Univ. .
  • Mudrov , V. I. , Kushko , V. L. , Mikhailov , V. I. and Osovitskii , E. M. 1968 . Some experiments on the use of the least-moduli method in processing orbital data . Cosmic Res. , 6 : 421 – 431 .
  • Narula , S. C. and Wellington , J. F. 1977a . Algorithm AS108. Multiple linear regression with minimun sum of absolute errors . Appl. Statist. , 26 : 106 – 111 .
  • Narula , S. C. and Wellington , J. F. 1977b . Prediction, linear regression and minimum sum of relative errors . Technometrics , 19 : 185 – 190 .
  • Narula, S. C. & Wellington, J. F. (1977c). Subset selection with minimum sum of weighted absolute errors. Tech. Report No. 37-77-P10, School of Managment, Rensselaer Polytechnic Inst., Troy, New York.
  • Narula , S. C. and Wellington , J. F. 1977d . An algorithm for the minimum sum of weighted absolute error regression . Commun. Statist. B. , 6 (This issue)
  • Osborne , M. R. 1972 . A class of methods for minimizing a sum of squares . Aust. Computer J. , 4 : 164 – 169 .
  • Osborne , M. R. and Watson , G. A. 1971 . On an algorithm for discrete nonlinear L1 approximation . Comp. J. , 14 : l84 – 188 .
  • Oveson, R. M. (1969). Regression Parameter Estimation by Minimizing the Sum of Absolute Errors. Unpublished Ph.D. thesis. Harvard Univ., Cambridge, Massachusetts.
  • Pfaffenberger , R. C. and Dinkel , J. J. 1978 . “ Absolute deviations curve fitting: an alternative to least squares ” . In Contributions to Survey Sampling and Applied Statistics , Edited by: David , H. A. New York : Academic Press . (To appear)
  • Rabinowitz , P. 1968 . Applications of linear programming to numerical analysis . SIAM Rev. , 10 : 121 – 159 .
  • Rao , M. R. and Shrinivasan , V. 1972 . A note on Sharpe’s algorithm for minimizing the sum of absolute deviations in a simple regression problem . Management Sci. , 19 : 222 – 225 .
  • Rhodes , E. C. 1930 . Reducing observations by the method of minimum deviations . Phil. Mag. (7th Series) , 9 : 974 – 992 .
  • Rice , J. R. 1964 . The Approximation of Functions, Volume I: Linear Theory , Reading, Mass : Addison-Wesley Pub. Co. .
  • Rice , J. R. and White , J. S. 1964 . Norms for smoothing and estimation . SIAM Rev. , 6 : 243 – 256 .
  • Robers , P. D. and Ben-Israel , A. 1969 . An interval programming algorithm for discrete linear L1 approximation problems . J. Approx. Theory , 2 : 323 – 336 .
  • Robers , P. D. and Robers , S. S. 1973 . Algorithm 458: Discrete linear L1 approximation by interval linear programming . Commun. Assoc. Comput. Mach. , l6 : 629 – 631 .
  • Roodman , G. 1974 . A procedure for optimal stepwise MSAE regression analysis . Operat. Res. , 22 : 393 – 399 .
  • Rosenberg , B. and Carlson , D. 1970 . “ The sampling distribution of least absolute residuals regression estimates ” . In Working Paper No. IP-164, Center for Research in Management Science , Berkeley, California : Univ. of California .
  • Rosenberg , B. and Carlson , D. 1977 . A Simple Approximation of the Sampling Distribution of Least Absolute Residuals Regression Estimates . Commun. Statist. B , 6 (This issue)
  • Sadovski , A. N. 1974 . Algorithm AS74. L1-norm fit of a straight line . Appl. Statist. , 23 : 244 – 248 .
  • Schlossmacher , E. J. 1973 . An iterative technique for absolute deviations curve fitting . J. Amer. Statist. Assoc. , 68 : 857 – 859 .
  • Schmitz , N. 1973 . Proceedings of the Fourth Conference on Probability Theory . On the use of linear programming methods in statistics. (German.) . 1973 , Bucharest. pp. 343 – 353 .
  • Sharpe , W. F. 1971 . Mean-absolute-deviation characteristic lines for securities and portfolios . Management Sci. , 18 B1 – B13 .
  • Shier , D. and Witzgall , C. 1977 . Norm approximation problems and norm statistics . Nat. Bur. Stand. J. Res. B. , To appear
  • Sielken , R. L. and Hartley , H. O. 1973 . Two linear programming algorithms for unbiased estimation of linear models . J. Amer. Statist. Assoc. , 68 639 – 641 .
  • Singleton , R. R. 1940 . A method of minimizing the sum of absolute values of deviations . Ann. Math. Statist. , 11 301 – 310 .
  • Sposito , V. A. 1975 . Linear and Nonlinear Programming , Ames : Iowa State University Press .
  • Sposito , V. A. , Kennedy , W. J. and Gentle , J. E. 1977 . Algorithm AS110: Lp norm fit of a straight Line . Appl. Statist. , 26 : 114 – 118 .
  • Sposito , V. A. , Mc Cormick , G. F. and Kennedy , W. J. 1975 . Proceedings of the Eighth Symposium on the Interface . L1 estimation strategies based on the simplex algorithm . 1975 . Los Angeles : Health Science Computing Facility, UCLA . (J. W. Frane, Ed.)
  • Sposito , V. A. and Smith , W. C. 1976 . On a sufficient and a necessary condition for L1 estimation . Appl. Statist. , 25 : 154 – 157 .
  • Stigler , S. M. 1973 . Studies in the history of probability and statistics, XXXII: Laplace, Fisher, and the discovery of sufficiency . Biometrika , 60 : 439 – 445 .
  • Spyropoulos , K. , Kiountouzis , E. and Young , A. 1973 . Discrete approximation in the L1 norm . Computer J. , 16 : 18 – 26 .
  • Taylor , L. D. 1973 . “ Estimation by minimizing the sum of absolute errors ” . In Frontiers in Econometrics , Edited by: Zarembka , P. New York : Academic Press .
  • Tukey , J. W. 1962 . The future of data analysis . Ann. Math. Statist. , 33 : 1 – 67 .
  • Turner , H. H. 1887 . On Mr. Edgeworth’s method of reducing observations relating to several quantities . phil. Mag. (5th Series) , 24 : 466 – 470 .
  • Usow , K. H. 1967 . On L1 approximation II: Computation for discrete functions and discretization effects . SIAM J. Numer. Anal. , 4 : 233 – 244 .
  • Wagner , H. M. 1959 . Linear programming techniques for regression analysis . J. Amer. Statist. Assoc. , 54 : 206 – 212 .
  • Wagner , H. M. 1962 . Nonlinear regression with minimal assumptions . J. Amer. Statist. Assoc. , 57 : 572 – 578 .
  • Walsh , J. L. 1959 . On extremal approximations. On Numerical Approximation , Edited by: Langer , R. E. Madison : University of Wisconsin Press .
  • Watson , G. A. 1973 . The calculation of best linear one-sided Lp approximations . Math. Comput. , 27 : 607 – 620 .
  • Young , J. D. 1971 . Smoothing data with tolerances by use of linear programming . J. Inst. Math. Appl. , 8 : 69 – 79 .
  • Zorilescu , D. 1970 . The calculation of regressions with the aid of the simplex method . Studil Cercretari Mat. , 22 : 209 – 212 . (Romanian, French summary.)

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.