[PDF] Least Absolute Deviations Curve Fitting eBook

Author : P- Bloomfield
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 49,1 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1468485741

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Least squares is probably the best known method for fitting linear models and by far the most widely used. Surprisingly, the discrete L 1 analogue, least absolute deviations (LAD) seems to have been considered first. Possibly the LAD criterion was forced into the background because of the com putational difficulties associated with it. Recently there has been a resurgence of interest in LAD. It was spurred on by work that has resulted in efficient al gorithms for obtaining LAD fits. Another stimulus came from robust statistics. LAD estimates resist undue effects from a feyv, large errors. Therefore. in addition to being robust, they also make good starting points for other iterative, robust procedures. The LAD criterion has great utility. LAD fits are optimal for linear regressions where the errors are double exponential. However they also have excellent properties well outside this narrow context. In addition they are useful in other linear situations such as time series and multivariate data analysis. Finally, LAD fitting embodies a set of ideas that is important in linear optimization theory and numerical analysis. viii PREFACE In this monograph we will present a unified treatment of the role of LAD techniques in several domains. Some of the material has appeared in recent journal papers and some of it is new. This presentation is organized in the following way. There are three parts, one for Theory, one for Applicatior.s and one for Algorithms.

Author : Dongdong Lei
Publisher :
Page : 8 pages
File Size : 38,78 MB
Release : 2001
Category :
ISBN :

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The least absolute deviations criterion, or the l1 norm, is frequently used for approximation where the data may contain outliers or wild points'. One of the most popular methods for solving the least absolute deviations data fitting problem is the Barrodale and Roberts (BR) algorithm (1973), which is based on linear programming techniques and the use of a modified simplex method. This algorithm is particularly efficient. However, since it is based upon the simplex method it can be susceptible to the accumulation of unrecoverable rounding errors caused by using an inappropriate pivot. In this paper we shall show how we can extend a numerically stable form of the simplex method to the special case of l1 approximation whilst still maintaining the efficiency of the Barrodale and Roberts algorithm. This extension is achieved by using the l1 characterization to rebuild the relevant parts of the simplex tableau at each iteration. The advantage of this approach is demonstrated most effectively when the observation matrix of the approximation problem is sparse, as in the case when using compactly supported basis functions such as B-splines. Under these circumstances the new method is considerably more efficient than the Barrodale and Roberts algorithm as well as being more robust.

Author : Peter Bloomfield
Publisher : Birkhäuser
Page : 351 pages
File Size : 21,94 MB
Release : 2012-12-12
Category : Mathematics
ISBN : 9781468485769

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Least squares is probably the best known method for fitting linear models and by far the most widely used. Surprisingly, the discrete L 1 analogue, least absolute deviations (LAD) seems to have been considered first. Possibly the LAD criterion was forced into the background because of the com putational difficulties associated with it. Recently there has been a resurgence of interest in LAD. It was spurred on by work that has resulted in efficient al gorithms for obtaining LAD fits. Another stimulus came from robust statistics. LAD estimates resist undue effects from a feyv, large errors. Therefore. in addition to being robust, they also make good starting points for other iterative, robust procedures. The LAD criterion has great utility. LAD fits are optimal for linear regressions where the errors are double exponential. However they also have excellent properties well outside this narrow context. In addition they are useful in other linear situations such as time series and multivariate data analysis. Finally, LAD fitting embodies a set of ideas that is important in linear optimization theory and numerical analysis. viii PREFACE In this monograph we will present a unified treatment of the role of LAD techniques in several domains. Some of the material has appeared in recent journal papers and some of it is new. This presentation is organized in the following way. There are three parts, one for Theory, one for Applicatior.s and one for Algorithms.

Author : R. D. Armstrong
Publisher :
Page : 17 pages
File Size : 17,83 MB
Release : 1975
Category :
ISBN :

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A comparison is made between linear programming and weighted least squares approach to absolute deviation curve fitting. The computational results are consistent in showing linear programming substantially reduces solution times while requiring only a relatively small amount of additional storage.

Author : Joong Hoon Kim
Publisher : Springer
Page : 456 pages
File Size : 41,66 MB
Release : 2015-08-08
Category : Computers
ISBN : 3662479265

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The Harmony Search Algorithm (HSA) is one of the most well-known techniques in the field of soft computing, an important paradigm in the science and engineering community. This volume, the proceedings of the 2nd International Conference on Harmony Search Algorithm 2015 (ICHSA 2015), brings together contributions describing the latest developments in the field of soft computing with a special focus on HSA techniques. It includes coverage of new methods that have potentially immense application in various fields. Contributed articles cover aspects of the following topics related to the Harmony Search Algorithm: analytical studies; improved, hybrid and multi-objective variants; parameter tuning; and large-scale applications. The book also contains papers discussing recent advances on the following topics: genetic algorithms; evolutionary strategies; the firefly algorithm and cuckoo search; particle swarm optimization and ant colony optimization; simulated annealing; and local search techniques. This book offers a valuable snapshot of the current status of the Harmony Search Algorithm and related techniques, and will be a useful reference for practising researchers and advanced students in computer science and engineering.

Author : Helmuth Späth
Publisher : Academic Press
Page : 338 pages
File Size : 42,46 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483264548

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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.

Author : Shennan Ye
Publisher :
Page : 66 pages
File Size : 23,17 MB
Release : 2012
Category : Boosting (Algorithms)
ISBN :

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For its simplicity and elegant theoretical properties, Least Squares (LS) regression has been used as a primary tool for a long time. However, it is well known that LS regression is very sensitive to the presence of unusual points in the data used to fit a model. As an alternative to LS regression, this thesis studied the properties and fitting algorithms for Least Absolute Deviations (LADs) regression model. Two optimization methods were investigated for fitting the model of LAD. The first one made use of the weighted median computation in each step, and iteratively estimated the coefficients to minimize the loss function. The second method applied functional gradient descent in each iteration, and built the model incrementally. The experiments on simulated data and real world data were performed, and the performance of these two methods was compared in terms of algorithm efficiency and prediction accuracy. The result of comparison showed that although both techniques work well to minimize the loss function, it is sufficient to say that compared to weighted median method, gradient descent method has a better performance not only on efficiency but also on the accuracy.

Author : Richard A. Ashley
Publisher : Wiley Global Education
Page : 740 pages
File Size : 31,78 MB
Release : 2012-04-13
Category : Business & Economics
ISBN : 1118213513

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Fundamentals of Applied Econometrics is designed for an applied, undergraduate econometrics course providing students with an understanding of the most fundamental econometric ideas and tools. The text serves both the student whose interest is in understanding how one can use sample data to illuminate economic theory and the student who wants and needs a solid intellectual foundation on which to build practical experiential expertise. Divided into two parts, the first half provides a thorough undergraduate-level treatment of multiple regressions including an extensive statistics review with integrated, hands-on Acting Learning Exercises so students learn by doing. The second half of the book covers a number of advanced topics: panel data modeling, time series analysis, binary-choice modeling, and an introduction to GMM. This latter portion of the book is very suitable for a more advanced course: a second-term undergraduate course, a Masters level course, or as a companion reading for a Doctoral level course.