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Solve least absolute value regression problems using modified goal programming techniques

COMPUTERS & OPERATIONS RESEARCH 1998年第12期25卷 1137-1143页

作者： Li, HL Natl Chiao Tung Univ Inst Informat Management Hsinchu 30050 Taiwan

Highlights a study which used the markedly lower number of deviational variables to reformulate the least absolute valve (LAV) regression problem, used in estimation of regression equations. Development of linear programs and numerous algorithms to solve the LAV regression problem; What is the LAV regression problem; Methodology used to conduct the study; Results of the study.

关键词： goal programming least absolute value regression

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A BOOTSTRAP APPROACH TO HYPOTHESIS-TESTING IN least absolute value regression

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 1995年第2期20卷 119-130页

作者： DIELMAN, TE ROSE, EL TEXAS CHRISTIAN UNIV MJ NEELEY SCH BUSINESSFT WORTHTX 76129 UNIV SO CALIF SCH BUSINESS ADMLOS ANGELESCA 90089

This study compares three alternative procedures for testing the significance of coefficients in least absolute value (LAV) regression, in the context of small samples. The three tests considered are: the likelihood ratio test using an estimator of the nuisance parameter proposed by McKean and Schrader (Comm. Statist. Simulation Comput. 13 (1984)), the Lagrange multiplier test, and a bootstrap test in which critical values of the test statistic are obtained by resampling. Comparisons among the tests are made by considering both observed significance levels and power. The bootstrap test used in this study performs well, compared to the other two tests. This result is in contrast to results, involving a somewhat different use of the bootstrap technique, obtained by Dielman and Pfaffenberger (Comput. Statist, Data Anal, 14 (1992)), and suggests that the use of the technique proposed in this paper has strong potential for applicability in hypothesis testing for LAV regression.

关键词： least absolute value regression ROBUST regression L(1)-regression least absolute DEVIATIONS

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A NEW DESCENT ALGORITHM FOR THE least absolute value regression PROBLEM

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COMMUNICATIONS IN STATISTICS PART B-SIMULATION AND COMPUTATION 1981年第5期10卷 479-491页

作者： WESOLOWSKY, GO McMaster University Hamilton Ontario Canada

This paper presents a new and simple algorithm for the least absolute value regression problem. It is based on the notion of “edge” descent along the surface of the objective function. It is comparable or better in ... 详细信息

关键词： least absolute value regression descent algorithm

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A note on hypothesis testing in LAV multiple regression: A small sample comparison

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 1997年第3期23卷 381-388页

作者： Dielman, TE Rose, EL TEXAS CHRISTIAN UNIV MJ NEELEY SCH BUSINESSFT WORTHTX 76129 UNIV SO CALIF SCH BUSINESS ADMLOS ANGELESCA 90089

We compare three approaches for assessing the significance of coefficients in least absolute value (LAV) multiple regression. The three test procedures studied are the Wald, likelihood ratio (LR), and Lagrange multiplier (LM) tests. Empirical levels of significance and power for the three test procedures are compared based on Monte Carlo simulation. This paper extends previous studies that concentrated only on simple regression. Further, the performance of overall goodness-of-fit tests for multiple regression is also examined, and a more extensive examination of the power of the tests is performed. The results of the study suggest that the LR and LM tests are preferable to the Wald test for this situation.

关键词： L(1)-regression least absolute value regression robust regression least absolute deviations Lagrange multiplier test likelihood ratio test Wald test

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A note on hypothesis testing in LAV multiple regression: A small sample comparison

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 1996年第4期21卷 463-470页

作者： Dielman, TE Rose, EL TEXAS CHRISTIAN UNIV MJ NEELEY SCH BUSINESSFT WORTHTX 76129 UNIV SO CALIF SCH BUSINESS ADMLOS ANGELESCA 90089

关键词： L(1)-regression least absolute value regression robust regression least absolute deviations Lagrange multiplier test likelihood ratio test Wald test

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A GLOBALLY AND QUADRATICALLY CONVERGENT AFFINE SCALING METHOD FOR LINEAR L(1) PROBLEMS

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MATHEMATICAL PROGRAMMING 1992年第2期56卷 189-222页

作者： COLEMAN, TF LI, YY CORNELL UNIV CTR APPL MATHITHACANY 14853

Recently, various interior point algorithms related to the Karmarkar algorithm have been developed for linear programming. In this paper, we first show how this "interior point" philosophy can be adapted to the linear l1 problem (in which there are no feasibility constraints) to yield a globally and linearly convergent algorithm. We then show that the linear algorithm can be modified to provide a globally and ultimately quadratically convergent algorithm. This modified algorithm appears to be significantly more efficient in practise than a more straightforward interior point approach via a linear programming formulation: we present numerical results to support this claim.

关键词： LINEAR L(1) ESTIMATION LINEAR PROGRAMMING INTERIOR-POINT ALGORITHM SIMPLEX METHOD least absolute value regression AFFINE SCALING METHOD KARMARKAR

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A FURTHER COMPARISON OF TESTS OF HYPOTHESES IN LAV regression

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 1992年第3期14卷 375-384页

作者： DIELMAN, TE PFAFFENBERGER, RC TEXAS CHRISTIAN UNIV MJ NEELEY SCH BUSINESSFT WORTHTX 76129

This study compares five alternate test procedures for the significance of coefficients in LAV regression. The WALD and LR tests using the SECI estimator of lambda proposed by McKean and Schrader (Commun. Statist. - Simulation Comput. 13 (1984) p. 751-773) were examined as well as versions of these tests using bootstrap estimates of lambda (BWALD and BLR) and the LM test. There is some evidence that the empirical level of significance for the LM test more nearly conforms to the expected level (5% used in study) than the observed levels do for the other tests. The two tests that appear to perform best in the experiment arc the LR test using the SECI estimator of lambda and the LM test. The bootstrap version of the LR test is computationally more expensive and appears to be no better (and perhaps worse in terms of the empirical size) than the traditional version. The WALD test appears inferior in the computations in either its traditional or bootstrap versions.

关键词： least absolute value regression ROBUST regression L1-regression least absolute DEVIATIONS

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