On L1 and Chebyshev estimation

DOI10.1007/BF01580112zbMath0271.41021MaRDI QIDQ3215733

C. S. Smith, Gautam M. Appa

Publication date: 1973

Published in: Mathematical Programming (Search for Journal in Brave)

Mathematics Subject Classification ID

Linear programming (90C05) Best approximation, Chebyshev systems (41A50)

Related Items (31)

Formulae for theL₀,L₁andL_∞Norms ⋮ A primal-dual homotopy algorithm for \(\ell _{1}\)-minimization with \(\ell _{\infty }\)-constraints ⋮ The determination of a ``least quantile of squares regression line for all quantiles ⋮ Influence measure for the L₁regression ⋮ A pure \(L_1\)-norm principal component analysis ⋮ Mixed \(L_p\) estimators variety for model order reduction in control oriented system identification ⋮ Computation of efficient solutions of discretely distributed stochastic optimization problems ⋮ L₁for the simple linear regression model ⋮ The historical development of the linear minimax absolute residual estimation procedure 1786--1960 ⋮ Estimating the parameters in regression with uniformly distributed errors ⋮ Non-asymptotic bounds for the \(\ell_{\infty}\) estimator in linear regression with uniform noise ⋮ Constrained \(l_ 1\) estimation via geometric programming ⋮ Linear facility location. Solving extensions of the basic problem ⋮ On l₁regression coeficients ⋮ On the invariance of certain estimators ⋮ Least absolute value and chebychev estimation utilizing least squares results ⋮ Lagrangian approach for large-scale least absolute value estimation ⋮ An algorithm for discrete chebychev curve fitting for the simple model using a dual linear programming approach ⋮ On least absolute values estimation ⋮ Extensions to a Best Subset Algorithm for Least Absolute Value Estimation ⋮ Complexity and applications of the homotopy principle for uniformly constrained sparse minimization ⋮ Comparison of mathematical programming software: A case study using discrete \(L_ 1\) approximation codes ⋮ On a class of interval predictor models with universal reliability ⋮ Fitting hyperplanes by minimizing orthogonal deviations ⋮ A linear programming algorithm for curve fitting in the L_∞norm ⋮ Goal programming models and their duality relations for use in evaluating security portfolio and regression relations ⋮ Useful generalized properties of L₁estimators ⋮ The best parameter subset using the Chebychev curve fitting criterion ⋮ A new technique for curve fitting based on minimum absolute deviations ⋮ Tight bounds for capacities ⋮ The linear regression model: L_pnorm estimation and the choice of p

Cites Work

• Über diskrete und lineare Tschebyscheff-Approximationen
• On the numerical determination of the best approximations in the Chebyshev sense
• Note on Jordan elimination, linear programming and Tchebyscheff approximation
• Algorithms for best \(L_ 1\) and \(L_ \infty\) linear approximations on a discrete set
• Optimal Estimation of Executive Compensation by Linear Programming
• Linear Programming Techniques for Regression Analysis
• The Small Sample Properties of Simultaneous Equation Least Absolute Estimators vis-a-vis Least Squares Estimators

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