A Monte Carlo study of the accuracy and robustness of ten bivariate location estimators

Massé, Jean–Claude; Plante, Jean‐François

doi:10.1016/s0167-9473(02)00103-2

Cited by 24 publications

(12 citation statements)

References 24 publications

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“…We observe that locations based on the mean are slightly influenced by the extreme values of the sample, for instance, in the series (Q, D). This result is in agreement with the study by Massé and Plante [2003] where the authors recommend, on the basis of accuracy and robustness, the use of spatial median followed by Oja and Tukey medians.…”

Section: Location Parameterssupporting

confidence: 92%

“…We consider the set E ⊆ R d of points that maximize the considered depth function. The depth median is the centeroid of the polygon composed by the set E of points maximizing the selected depth function [ Massé and Plante , 2003]. Generally, E is a convex and compact set [ León and Massé , 1993].…”

Section: Methodsmentioning

confidence: 99%

“…However, each sample feature was subsequently studied separately by a number of authors. For instance, the location was studied by Massé and Plante [2003], Zuo [2003] and Wilcox and Keselman [2004]; scale was treated by Li and Liu [2004], symmetry was the focus of Rousseeuw and Struyf [2004] and Serfling [2006] and kurtosis was addressed by Wang and Serfling [2005]. These studies focused mainly on inferential and asymptotical results.…”

Section: Introductionmentioning

confidence: 99%

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Depth-based multivariate descriptive statistics with hydrological applications

Chebana

Ouarda

2011

J. Geophys. Res.

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Hydrological events are often described through various characteristics which are generally correlated. To be realistic, these characteristics are required to be considered jointly. In multivariate hydrological frequency analysis, the focus has been made on modeling multivariate samples using copulas. However, prior to this step, data should be visualized and analyzed in a descriptive manner. This preliminary step is essential for all of the remaining analysis. It allows us to obtain information concerning the location, scale, skewness, and kurtosis of the sample as well as outlier detection. These features are useful to exclude some unusual data, to make different comparisons, and to guide the selection of the appropriate model. In the present paper we introduce methods measuring these features, which are mainly based on the notion of depth function. The application of these techniques is illustrated on two real‐world streamflow data sets from Canada. In the Ashuapmushuan case study, there are no outliers and the bivariate data are likely to be elliptically symmetric and heavy‐tailed. The Magpie case study contains a number of outliers, which are identified to be real observed data. These observations cannot be removed and should be accommodated by considering robust methods for further analysis. The presented depth‐based techniques can be adapted to a variety of hydrological variables.

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Section: Location Parameterssupporting

confidence: 92%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Depth-based multivariate descriptive statistics with hydrological applications

Chebana

Ouarda

2011

J. Geophys. Res.

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“…However, the skipped estimator studied here, which is location and scale equivariant, was found to perform reasonably well when testing (3) via a percentile bootstrap method that measures the depth of null vector using projection distances. Another possible appeal of the SP estimator over the DG estimator is that for light-tailed distributions, including normal distributions, the DG estimator has relatively poor efficiency (e.g., Massé & Plante, 2003;Wilcox, 2012, p. 251). In contrast, the SP estimator performs nearly as well as the usual sample mean.…”

Section: Resultsmentioning

confidence: 99%

Within Groups ANOVA When Using a Robust Multivariate Measure of Location

Wilcox¹,

Hayes²

2016

J. Mod. App. Stat. Meth.

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For robust measures of location associated with J dependent groups, various methods have been proposed that are aimed at testing the global hypothesis of a common measure of location applied to the marginal distributions. A criticism of these methods is that they do not deal with outliers in a manner that takes into account the overall structure of the data. Location estimators have been derived that deal with outliers in this manner, but evidently there are no simulation results regarding how well they perform when the goal is to test the some global hypothesis. The paper compares four bootstrap methods in terms of their ability to control the Type I error probability when the sample size is small, two of which were found to perform poorly. The choice of location estimator was found to be important as well. Indeed, for several of the estimators considered here, control over the Type I error probability was very poor. Only one estimator performed well when using the first of two general approaches that might be used. It is based on a variation of the (affine equivariant) Donoho-Gasko trimmed mean. For the second general approach, only a skipped estimator performed reasonably well. (It removes outliers via a projection method and averages the remaining data.) Only one bootstrap method was found to perform well when using the first approach. A different bootstrap method is recommended when using the second approach.

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“…So one may wish to replace the mean in the delay-andsum algorithm by a more robust estimator. Massé and Plante compared ten bivariate location estimators with a Monte Carlo study using 26 different noise distributions and concluded that the geometric median 'clearly stands as the best overall' [26]. The geometric median, also known as the spatial median, L 1 median or L 1 estimator, is defined as the point minimising the Euclidean distance to all data points, that is [27] Median {x k } = arg min…”

Section: Geometric Medianmentioning

confidence: 99%

On the Use of the Geometric Median in Delay-and-Sum Ultrasonic Array Imaging

Budyn

2020

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Delay-and-sum algorithms are imaging techniques in non-destructive testing which form images by summing backpropagated signals. Under this approach, a small number of high intensity signals, such as those from boundary reflections, may create artefacts which degrade the image and hinder defect detection. This paper introduces a probabilistic model of the summation which explains the origin of this effect and proposes to replace the summation in the imaging algorithm by the more statistically robust geometric median. As demonstrated on a experimental inspection using multi-view Total Focusing Method and Plane Wave Imaging, this novel technique effectively suppresses some artefacts, at the expense of an increase of the structural noise amplitude and additional diffraction artefacts at the ends of some structural features. As such the geometric median provides an alternative imaging approach that may improve performance in some circumstances.

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A Monte Carlo study of the accuracy and robustness of ten bivariate location estimators

Cited by 24 publications

References 24 publications

Depth-based multivariate descriptive statistics with hydrological applications

Depth-based multivariate descriptive statistics with hydrological applications

Within Groups ANOVA When Using a Robust Multivariate Measure of Location

On the Use of the Geometric Median in Delay-and-Sum Ultrasonic Array Imaging

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