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Mathematical Algorithms for Linear Regression
1st Edition - December 17, 1991
Author: Helmuth Späth
Editor: Werner Rheinboldt
9 7 8 - 1 - 4 8 3 2 - 6 4 5 4 - 7
Mathematical Algorithms for Linear Regression discusses numerous fitting principles related to discrete linear approximations, corresponding numerical methods, and FORTRAN 77… Read more
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Mathematical Algorithms for Linear Regression discusses numerous fitting principles related to discrete linear approximations, corresponding numerical methods, and FORTRAN 77 subroutines. The book explains linear Lp regression, method of the lease squares, the Gaussian elimination method, the modified Gram-Schmidt method, the method of least absolute deviations, and the method of least maximum absolute deviation. The investigator can determine which observations can be classified as outliers (those with large errors) and which are not by using the fitting principle. The text describes the elimination of outliers and the selection of variables if too many or all of them are given by values. The clusterwise linear regression accounts if only a few of the relevant variables have been collected or are collectible, assuming that their number is small in relation to the number of observations. The book also examines linear Lp regression with nonnegative parameters, the Kuhn-Tucker conditions, the Householder transformations, and the branch-and-bound method. The text points out the method of least squares is mainly used for models with nonlinear parameters or for orthogonal distances. The book can serve and benefit mathematicians, students, and professor of calculus, statistics, or advanced mathematics.
PrefaceNotationI IntroductionII Linear Lp Regession 2.1 Fundamentals 2.2 ρ = 2 (Method of the Least Squares: NGL, MGS, ICMGS, GIVR, HFTI, SVDR) 2.3 ρ ≠ 1,2, ∞ (LPREGR) 2.4 ρ = 1 (Method of Least Absolute Deviations: A478L1, AFKL1, BLOD1) 2.5 ρ = ∞ (Method of Least Maximum Absolute Deviation: A328LI, A495LI, ABDLI) 2.6 Comparison of Residuals (RES) and Choice of p 2.7 The Elimination of Outliers 2.8 Selection of Variables (SCR, SCRFL1) 2.9 Clusterwise Linear Regression (CWLL2R, CWLL1R, CWLLIR) 2.10 Average Linear Regression (AVLLSQ)III Robust Regression (ROBUST) 193IV Ridge Regression (RRL2, RRL1, RRL1)V Linear Lp Regression with Linear Constraints 5.1 Introduction 5.2 p = 2(CL2) 5.3 p = 1 (CL1) 5.4 ρ = ∞ (CLI)VI Linear Lp Regression with Nonnegative Parameters (p = 2: NNLS; p = 1: NNL1; p = ∞: NNL1)VII Orthogonal Linear Lp Regression 7.1 Fundamentals 7.2 p = 2(L2ORTH) 7.3 p ≠ 1,2, ∞ (LPORTH) 7.4 p = 1 (L1ORTH) 7.5 p = ∞ (L1ORTH) 7.6 Comparison of Residuals and Choice of p 7.7 Orthogonal L2 Regression with Linear Manifolds (LMORTH)Final RemarksList of SubroutinesAppendix: ExamplesIndex