Fast Very Robust Methods for the Detection of Multiple Outliers

Atkinson, Anthony C.

doi:10.2307/2290995

Cited by 99 publications

(66 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Then, pointwise values of such distribution yield to quantile estimation of the exact probability. Such method, that we also have used in our simulations, is referred to as "simulated envelopes", and it was originally introduced by Atkinson (1994). Simulating the envelopes increases considerably the computing time and, from results of our Monte Carlo experiment discussed later, we have not found any significant difference.…”

Section: Preliminaries and Backgroundmentioning

confidence: 79%

Robust estimation of efficient mean–variance frontiers

Grossi¹,

Laurini²

2011

Adv Data Anal Classif

View full text Add to dashboard Cite

show abstract

Section: Preliminaries and Backgroundmentioning

confidence: 79%

Robust estimation of efficient mean–variance frontiers

Grossi¹,

Laurini²

2011

Adv Data Anal Classif

View full text Add to dashboard Cite

show abstract

“…Barnett and Lewis 2000;Gather and Becker 1997;Rocke and Woodruff 1996;Atkinson 1994; Bartkowiak and Szustalewicz 1997 and references therein). One general approach consists of calculating some measure of distance for each observation which in some sense characterizes its similarity with respect to the rest of the data.…”

Section: Outlier Detection and Robust Estimationmentioning

confidence: 99%

The flood algorithm—a multivariate, self-organizing-map-based, robust location and covariance estimator

2011

View full text Add to dashboard Cite

Self-organizing maps (SOMs) introduced by Kohonen (Biol. Cybern. 43(1): [59][60][61][62][63][64][65][66][67][68][69] 1982) are well-known in the field of artificial neural networks. The way SOMs are performing is very intuitive, leading to great popularity and numerous applications (related to statistics: classification, clustering). The result of the unsupervised learning process performed by SOMs is a non-linear, low-dimensional projection of the high-dimensional input data, that preserves certain features of the underlying data, e.g. the topology and probability distribution (Lee and Verleysen in Nonlinear Dimensionality Reduction, Springer, 2007; Kohonen in Selforganizing Maps, 3rd edn., Springer, 2001).With the U-matrix Ultsch (Information and Classification: Concepts, Methods and Applications, pp. 307-313, Springer, 1993) introduced a powerful visual representation of the SOM results. We propose an approach that utilizes the U-matrix to identify outlying data points. Then the revised subsample (i.e. the initial sample minus the outlying points) is used to give a robust estimation of location and scatter.

show abstract

“…Due to the major influence of outliers on most parametric tests, considerable attention has been devoted to the detection and accommodation of outliers (i.e. Andrews 1974;Tukey 1977;Atkinson 1994;Schwertman et al 2004, Das andBasudhar 2006). Tukey (1977) suggested a simple graphical method for identifying outliers that is based on the box-plot and involves the construction of ''inner fences'' and ''outer fences''.…”

Section: Sample Collection and Analysesmentioning

confidence: 99%

Spatial interpolation of severely skewed data with several peak values by the approach integrating kriging and triangular irregular network interpolation

Luo

et al. 2010

Environ Earth Sci

View full text Add to dashboard Cite

It was not unusual in soil and environmental studies that the distribution of data is severely skewed with several high peak values, which causes the difficulty for Kriging with data transformation to make a satisfied prediction. This paper tested an approach that integrates kriging and triangular irregular network interpolation to make predictions. A data set consisting of total Copper (Cu) concentrations of 147 soil samples, with a skewness of 4.64 and several high peak values, from a copper smelting contaminated site in Zhejiang Province, China. The original data were partitioned into two parts. One represented the holistic spatial variability, followed by lognormal distribution, and then was interpolated by lognormal ordinary kriging. The other assumed to show the local variability of the area that near to high peak values, and triangular irregular network interpolation was applied. These two predictions were integrated into one map. This map was assessed by comparing with rank-order ordinary kriging and normal score ordinary kriging using another data set consisting of 54 soil samples of Cu in the same region. According to the mean error and root mean square error, the approach integrating lognormal ordinary kriging and triangular irregular network interpolation could make improved predictions over rank-order ordinary kriging and normal score ordinary kriging for the severely skewed data with several high peak values.

show abstract

Fast Very Robust Methods for the Detection of Multiple Outliers

Cited by 99 publications

References 16 publications

Robust estimation of efficient mean–variance frontiers

Robust estimation of efficient mean–variance frontiers

The flood algorithm—a multivariate, self-organizing-map-based, robust location and covariance estimator

Spatial interpolation of severely skewed data with several peak values by the approach integrating kriging and triangular irregular network interpolation

Contact Info

Product

Resources

About