Linear programming approach to LMS-estimation

Bocek, Pavel; Lachout, Petr

doi:10.1016/0167-9473(93)e0051-5

Cited by 8 publications

(4 citation statements)

References 3 publications

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“…It started with the paper by Hettmansperger and Sheather (1992) showing by a case study that Least Median of Squares estimator (L M S) (Rousseeuw 1984) changes a lot its value when small change data is made. Their result was due to a bad algorithm, they used, and Víšek (1994) corrected the result employing the algorithm by Boček and Lachout (1995). However the phenomenon really exists, for the theoretical explanation see Víšek (1996bVíšek ( , 2000a.…”

Section: Why the Implicit Weighting Of Residualsmentioning

confidence: 94%

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Consistency of the instrumental weighted variables

Víšek

2007

Ann Inst Stat Math

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Section: Why the Implicit Weighting Of Residualsmentioning

confidence: 94%

“…We have mentioned the algorithm for the L M S by Boček and Lachout (1995) based on simplex method. Similarly, the algorithm for LT S was discussed and successfully tested in Víšek (1996bVíšek ( , 2000a.…”

Section: Algorithm For the Instrumental Weighted Variablesmentioning

confidence: 99%

Consistency of the instrumental weighted variables

Víšek

2007

Ann Inst Stat Math

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“…Bocek and Lachout [4] have proposed a linear programming technique as an alternative approximation algorithm to the LMS estimate. Convex quadratic programming formulations have been proposed by Musicant and Mangasarian [14] for Huber estimator.…”

Section: Brief Reviewmentioning

confidence: 99%

Deleting Outliers in Robust Regression with Mixed Integer Programming

Zioutas

Avramidis

2005

Acta Mathematicae Applicatae Sinica, English Series

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In robust regression we often have to decide how many are the unusual observations, which should be removed from the sample in order to obtain better fitting for the rest of the observations. Generally, we use the basic principle of LTS, which is to fit the majority of the data, identifying as outliers those points that cause the biggest damage to the robust fit. However, in the LTS regression method the choice of default values for high break down-point affects seriously the efficiency of the estimator. In the proposed approach we introduce penalty cost for discarding an outlier, consequently, the best fit for the majority of the data is obtained by discarding only catastrophic observations. This penalty cost is based on robust design weights and high break down-point residual scale taken from the LTS estimator. The robust estimation is obtained by solving a convex quadratic mixed integer programming problem, where in the objective function the sum of the squared residuals and penalties for discarding observations is minimized. The proposed mathematical programming formula is suitable for small-sample data. Moreover, we conduct a simulation study to compare other robust estimators with our approach in terms of their efficiency and robustness.

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“…A difficult problem in robust statistics estimation, and in particular in robust regression, is that of computing estimators based on minimization of the k th smallest value of absolute residuals, because of their combinatorial complexity (Bocvek and Lachout, 1995). It can be verified that the MMDR model is a specific case of this kind of problem (Reyna, 2001).…”

Section: Computational Implementationmentioning

confidence: 99%

Optimal Portfolio Structuring in Emerging Stock Markets Using Robust Statistics

Reyna¹,

Júnior

Mendes

et al. 2005

Brazilian Review of Econometrics

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Emerging markets are known to have unique characteristics when compared to more developed markets. The direct use of standard mathematical models proposed and tested in more developed markets is not always recommended in emerging markets. Extreme events in emerging markets have already been verified to distort the results obtained when using standard mathematical models in several situations, including optimal portfolio structuring. Practitioners working in the asset management industry in emerging markets have not yet incorporated optimization models into their routine. One of the reasons for that is that extreme events and/or economic discontinuities (such as the Brazilian and the Argentinean devaluation crises etc.) modify the financial environment in such a way that past data become of little use when looking forward. In this article we concentrate on proposing a methodology to handle extreme events. Two numerical examples taken from the Brazilian stock market are used to illustrate the use of our proposal.

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Linear programming approach to LMS-estimation

Cited by 8 publications

References 3 publications

Consistency of the instrumental weighted variables

Consistency of the instrumental weighted variables

Deleting Outliers in Robust Regression with Mixed Integer Programming

Optimal Portfolio Structuring in Emerging Stock Markets Using Robust Statistics

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