Robust two-group discrimination by bounded influence regression. A Monte Carlo simulation

Todorov, Valentin; Neykov, N. M.; Neytchev, P. N.

doi:10.1016/0167-9473(94)90122-8

Cited by 15 publications

(10 citation statements)

References 6 publications

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“…Both QDA and LDA using the classical estimates in (16) and (18) are vulnerable to the presence of outliers. The problem of the non-robustness of the classical estimates in the setting of the quadratic and linear discriminant analysis has been addressed by many authors: Todorov et al (1990Todorov et al ( , 1994a replaced the classical estimates by MCD estimates; Chork and Rousseeuw (1992) used MVE instead; Hawkins and McLachlan (1997) defined the minimum within-group covariance determinant estimator (MWCD) especially for the case of linear discriminant analysis; He and Fung (2000) and Croux and Dehon (2001) used S estimates;Hubert and Van Driessen (2004) applied the MCD estimates computed by the FAST-MCD algorithm. For a recent review and comparison of these methods see Todorov and Pires (2007).…”

Section: Linear and Quadratic Discriminant Analysismentioning

confidence: 99%

See 1 more Smart Citation

An Object-Oriented Framework for Robust Multivariate Analysis

Todorov¹,

Filzmoser²

2009

J. Stat. Soft.

Self Cite

301

197

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Taking advantage of the S4 class system of the programming environment R, which facilitates the creation and maintenance of reusable and modular components, an objectoriented framework for robust multivariate analysis was developed. The framework resides in the packages robustbase and rrcov and includes an almost complete set of algorithms for computing robust multivariate location and scatter, various robust methods for principal component analysis as well as robust linear and quadratic discriminant analysis. The design of these methods follows common patterns which we call statistical design patterns in analogy to the design patterns widely used in software engineering. The application of the framework to data analysis as well as possible extensions by the development of new methods is demonstrated on examples which themselves are part of the package rrcov.

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Section: Linear and Quadratic Discriminant Analysismentioning

confidence: 99%

“…This method, using MVE and MCD estimates, was proposed by Todorov et al (1990Todorov et al ( , 1994a and was also used, based on the MVE estimator by Chork and Rousseeuw (1992). Croux and Dehon (2001) applied this procedure for robustifying linear discriminant analysis based on S estimates.…”

Section: Computing the Common Covariance Matrixmentioning

confidence: 99%

An Object-Oriented Framework for Robust Multivariate Analysis

Todorov¹,

Filzmoser²

2009

J. Stat. Soft.

Self Cite

301

197

View full text Add to dashboard Cite

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“…Procedures are as followed [6]- [10]: 1) To analyze the problem existing in new product design, and define the relationship between design variables X and response output as a response surface model    …”

Section: Monte Carlo Methodsmentioning

confidence: 99%

“…Here we create the OptQuest model and run simulation experiments 1500 times according to distribution characteristics of design variables and constraints condition [4]- [6], and get the optimum of design variables , , , , showed, so design robustness of pressure container has been further improved than that of last time. .…”

Section: ) Design Optimizationmentioning

confidence: 99%

A Monte Carlo Based Robustness Optimization Method in New Product Design Process: A Case Study

Che

Wang²,

Li³

2014

AJIBM

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Monte Carlo method can analyze, solve and optimize many mathematical or physical problems through generating a large number of statistical random samples to simulating stochastic events. It also can be used to remarkably improve design quality of new product. In new product design process, setting distribution characteristics of the design variables is vital to product quality and production robustness. Firstly, response surface model between output characteristics and design variables in new product design is proposed, and the distribution characteristics of design variables and response output are analyzed; then position error model of response output and standard value and allowed error maximum is presented; and then the differences of position error model and allowed error maximum are counted, and reliability ratio is built and calculated, and design robustness of the new product is increased by adjusting the precision value of random design variables in Monte Carlo experiments. Finally, a case is brought forward to verify the validity of the method.

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“…Linear discriminant analysis procedures that are robust (i.e., insensitive) to departures from the assumption of multivariate normality have been proposed (Todorov, Neykov, & Neytchev, 1994) by replacing the conventional least-squares estimators of means and covariances with robust estimators, such as M-estimators (Croux & Dehon, 2001), minimum covariance determinant (MCD) estimators (Hubert & Van Driessen, 2004;Rousseeuw, 1984), minimum volume ellipsoid (MVE) estimators (Rousseeuw, 1984), and trimmed estimators (Ahmed & Lachenbruch, 1977;Gnanadesikan & Kettenring, 1972;Srivastava & Mudholkar, 2001). However, their emphasis has been primarily on prediction and not on describing the variables that contribute to group separation in non-normal data.…”

Section: Introductionmentioning

confidence: 99%