An Object-Oriented Framework for Robust Multivariate Analysis

Todorov, Valentin; Filzmoser, Peter

doi:10.18637/jss.v032.i03

Cited by 301 publications

(208 citation statements)

References 63 publications

(94 reference statements)

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“…Light, orange ellipses in the first three plots show the (t * , S * ) obtained using the best subset found by the FastMCD, FastMVE and SDE. These were computed with the R package rrcov [11], using default settings; 500 starting p-subsets (for the first two), and 500 directions a m (for SDE); and h = 51 (see Section 3.4) in all cases.…”

Section: 1mentioning

confidence: 99%

Finding multivariate outliers with FastPCS

Vakili¹,

Schmitt²

2014

Computational Statistics & Data Analysis

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The Projection Congruent Subset (PCS) is a new method for finding multivariate outliers. Like many other outlier detection procedures, PCS searches for a subset which minimizes a criterion. The difference is that the new criterion was designed to be insensitive to the outliers. PCS is supported by FastPCS, a fast and affine equivariant algorithm which is also detailed. Both an extensive simulation study and a real data application from the field of engineering show that FastPCS performs better than its competitors.

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Section: 1mentioning

confidence: 99%

Finding multivariate outliers with FastPCS

Vakili¹,

Schmitt²

2014

Computational Statistics & Data Analysis

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“…It simply replaces each observation with its rank (componentwise) over all groups and then applies Wilks' Lambda. The second test (Todorov and Filzmoser, 2010) uses a test statistic based on weighted MCD estimators and obtains the null distribution by Monte Carlo simulation from a multivariate normal distribution, as implemented in the R-package rrcov (Todorov and Filzmoser 2009). For both the classical test and its rank-transformed version, the approximation…”

Section: Finite-sample Robustness Of the Levelmentioning

confidence: 99%

Robust and Efficient One-Way MANOVA Tests

Aelst

Willems

2011

Journal of the American Statistical Association

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We propose robust tests as alternatives to the classical Wilks' Lambda test in one-way MANOVA. The robust tests use highly robust and efficient multi-sample multivariate S-or MM-estimators instead of the empirical covariances. The properties of several robust test statistics are compared. Under the null hypothesis, the distribution of the test statistics is proportional to a chi-square distribution. As an alternative to the asymptotic distribution, we develop a fast robust bootstrap method to estimate the distribution under the null hypothesis. We show when it is asymptotically correct to estimate the null distribution in this way and we use simulations to verify the performance of the bootstrap based tests in finite samples. We also investigate the power of the new tests, as well as their robustness against outliers. Finally, we illustrate the use of these robust test statistics on a real data example. Some additional results are provided as supplemental material.

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“…Therefore, estimation of location and scale parameters for a multivariate dataset can be done using the MCD method, which provides a high breakdown point. The robust version of the PCA can be obtained by substituting the and parameters with ̂and ̂ robust estimates [10].…”

Section: Introductionmentioning

confidence: 99%

Robust Principal Component Analysis based on Fuzzy Coded Data

Alkan¹,

Ganik²

2017

ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY a - Applied Sciences and Engineering

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In the presence of outliers in the dataset, the principal component analysis method, like many of the classical statistical methods, is severely affected. For this reason, if there are outliers in dataset, researchers tend to use alternative methods. Use of fuzzy and robust approaches is the leading choice among these methods. In this study, a new approach to robust fuzzy principal component analysis is proposed. This approach combines the power of both robust and fuzzy methods at the same time and collects these two approaches under the framework of principal component analysis. The performance of proposed approach called robust principal component analysis based on fuzzy coded data is examined through a set of artificial dataset that are generated by considering three different scenarios and a real dataset to observe how it is affected by the increase in sample size and changes in the rate of outliers. In light of the study's findings, it is seen that the proposed approach gives better results than the ones in the classical and robust principal component analysis in the presence of outliers in dataset.

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An Object-Oriented Framework for Robust Multivariate Analysis

Cited by 301 publications

References 63 publications

Finding multivariate outliers with FastPCS

Finding multivariate outliers with FastPCS

Robust and Efficient One-Way MANOVA Tests

Robust Principal Component Analysis based on Fuzzy Coded Data

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