An introduction to L 1 -norm based statistical data analysis

[1]  H. H. Turner M.A. B.Sc. LX. On Mr. Edgeworth's method of reducing observations relating to several quantities , 1887 .

[2]  E. C. Rhodes D.Sc. LXXXIX. Reducing observations by the method of minimum deviations , 1930 .

[3]  R. Singleton A Method for Minimizing the Sum of Absolute Values of Deviations , 1940 .

[4]  G. Box NON-NORMALITY AND TESTS ON VARIANCES , 1953 .

[5]  Abraham Charnes,et al.  Optimal Estimation of Executive Compensation by Linear Programming , 1955 .

[6]  O. J. Karst,et al.  Linear Curve Fitting Using Least Deviations , 1958 .

[7]  H. M. Wagner Linear Programming Techniques for Regression Analysis , 1959 .

[8]  E. Parzen On Estimation of a Probability Density Function and Mode , 1962 .

[9]  T. D. Wallace,et al.  A Sampling Study of Minimum Absolute Deviations Estimators , 1963 .

[10]  J. Rice,et al.  Norms for Smoothing and Estimation , 1964 .

[11]  P. J. Huber Robust Estimation of a Location Parameter , 1964 .

[12]  F. Hampel Contributions to the theory of robust estimation , 1968 .

[13]  Hrishikesh D. Vinod Mathematica Integer Programming and the Theory of Grouping , 1969 .

[14]  Robert E. Jensen,et al.  A Dynamic Programming Algorithm for Cluster Analysis , 1969, Oper. Res..

[15]  J. G. Hunt,et al.  The Small Sample Properties of Simultaneous Equation Least Absolute Estimators vis-a-vis Least Squares Estimators , 1970 .

[16]  F. Hampel A General Qualitative Definition of Robustness , 1971 .

[17]  P. J. Huber The 1972 Wald Lecture Robust Statistics: A Review , 1972 .

[18]  H. Harter The Method of Least Squares and Some Alternatives. , 1972 .

[19]  J. C. Dunn,et al.  A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters , 1973 .

[20]  S. Stigler Studies in the History of Probability and Statistics. XXXII Laplace, Fisher, and the discovery of the concept of sufficiency , 1973 .

[21]  E. Kiountouzis Linear Programming Techniques in Regression Analysis , 1973 .

[22]  H. O. Hartley,et al.  Two Linear Programming Algorithms for Unbiased Estimation of Linear Models , 1973 .

[23]  P. J. Huber Robust Regression: Asymptotics, Conjectures and Monte Carlo , 1973 .

[24]  I. Barrodale,et al.  An Improved Algorithm for Discrete $l_1 $ Linear Approximation , 1973 .

[25]  D. F. Andrews,et al.  A Robust Method for Multiple Linear Regression , 1974 .

[26]  P. Bickel One-Step Huber Estimates in the Linear Model , 1975 .

[27]  H. Harter The Method of Least Squares and Some Alternatives: Part III , 1975 .

[28]  H. Harter The Method of Least Squares and Some Alternatives. Addendum to Part IV , 1975 .

[29]  P-norm estimators in a linear regression model , 1976 .

[30]  R. Armstrong,et al.  A special purpose linear programming algorithm for obtaining least absolute value estimators in a linear model with dummy variables , 1977 .

[31]  Ronald D. Armstrong,et al.  An Algorithm for a Restricted Discrete Approximation Problem in the $L_1 $ Norm , 1977 .

[32]  Daryl E. Carlson,et al.  A simple approximation of the sampling distribution of least absolute residuals regression estimates , 1977 .

[33]  John W. Tukey,et al.  Exploratory Data Analysis. , 1979 .

[34]  Least absolute value regression: a special case of piecewise linear minimization , 1977 .

[35]  J. Gentle Least absolute values estimation: an introduction , 1977 .

[36]  John W. Hultz,et al.  Obtaining least absolute value estimates for a two-way classification model , 1977 .

[37]  I. Barrodale,et al.  An Efficient Algorithm for Discrete $l_1$ Linear Approximation with Linear Constraints , 1978 .

[38]  Ronald D. Armstrong,et al.  Least Absolute Value Estimates for a Simple Linear Regression Problem , 1978 .

[39]  John J. Dinkel,et al.  Absolute Deviations Curve Fitting: An Alternative to Least Squares , 1978 .

[40]  H. G. Wilson,et al.  LEAST SQUARES VERSUS MINIMUM ABSOLUTE DEVIATIONS ESTIMATION IN LINEAR MODELS , 1978 .

[41]  R. Koenker,et al.  Asymptotic Theory of Least Absolute Error Regression , 1978 .

[42]  A. Conn,et al.  Minimization Techniques for Piecewise Differentiable Functions: The l_1 Solution to an Overdetermined Linear System , 1978 .

[43]  Edward L. Frome,et al.  A revised simplex algorithm for the absolute deviation curve fitting problem , 1979 .

[44]  Nabih N. Abdelmalek,et al.  Algorithm 551: A Fortran Subroutine for the L1 Solution of Overdetermined Systems of Linear Equations [F4] , 1980, TOMS.

[45]  W. Steiger,et al.  Least Absolute Deviations Curve-Fitting , 1980 .

[46]  Yadolah Dodge,et al.  Mathematical Programming In Statistics , 1981 .

[47]  S. Stigler Gauss and the Invention of Least Squares , 1981 .

[48]  Roger Koenker,et al.  Tests of Linear Hypotheses and l[subscript]1 Estimation , 1982 .

[49]  L. Devroye The Equivalence of Weak, Strong and Complete Convergence in $L_1$ for Kernel Density Estimates , 1983 .

[50]  V. Sposito,et al.  L1Norm estimates for the simple regression problem , 1983 .

[51]  Asymptotic normality of p-norm estimators in multiple regression , 1984 .

[52]  T. E. Dielman,et al.  Least absolute value estimation in regression models: an annotated bibliography , 1984 .

[53]  W. Steiger,et al.  Least Absolute Deviations: Theory, Applications and Algorithms , 1984 .

[54]  L. Devroye,et al.  Nonparametric Density Estimation: The L 1 View. , 1985 .

[55]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[56]  Peter J. Huber,et al.  The place of the L1-norm in robust estimation , 1987 .

[57]  Peter J. Rousseeuw,et al.  Clustering by means of medoids , 1987 .

[58]  An application of L1 to astronomy , 1987 .

[59]  Asymptotic Properties of Restricted L1-Estimates of Regression , 1987 .

[60]  Subhash C. Narula,et al.  The Minimum Sum of Absolute Errors Regression , 1987 .

[61]  L. Devroye,et al.  Nonparametric density estimation : the L[1] view , 1987 .

[62]  A. Gaivoronski Numerical Techniques for Finding Estimates which Minimize the Upper Bound of the Absolute Deviation , 1987 .