Procedures for the identification of multiple influential observations in linear regression

Nurunnabi, Abdul; Hadi, Ali S.; Imon, A. H. M. Rahmatullah

doi:10.1080/02664763.2013.868418

Cited by 25 publications

(30 citation statements)

References 24 publications

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“…Martin, Roberts, and Zheng (2010) implemented delete-2 and delete-3 jackknife procedures and noted that delete-j approaches for j ≥ 4 will become workable with increased computing power. Another approach to identifying multiple influential observations, proposed by Nurunnabie, Nasser (2011) andNurunnabie, Hadi, andImon (2014), is the development of "group" influence measures that can be applied to a group of observations suspected of being influential. In the approaches proposed by Nurunnabie et al, the suspected group of observations is assumed to be provided by the data analyst or identified by some method for multivariate outlier detection.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive, Automatic Multiple-Case Deletion Technique for Detecting Influence in Regression

2014

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Critical to any regression analysis is the identification of observations that exert a strong influence on the fitted regression model. Traditional regression influence statistics such as Cook's distance and DFFITS, each based on deleting single observations, can fail in the presence of multiple influential observations if these influential observations "mask" one another, or if other effects such as "swamping" occur. Masking refers to the situation where an observation reveals itself as influential only after one or more other observations are deleted. Swamping occurs when points that are not actually outliers/influential are declared to be so because of the effects on the model of other unusual observations. One computationally expensive solution to these problems is the use of influence statistics that delete multiple rather than single observations. In this article, we build on previous work to produce a computationally feasible algorithm for detecting an unknown number of influential observations in the presence of masking. An important difference between our proposed algorithm and existing methods is that we focus on the data that remain after observations are deleted, rather than on the deleted observations themselves. Further, our approach uses a novel confirmatory step designed to provide a secondary assessment of identified observations. Supplementary materials for this article are available online.

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Section: Introductionmentioning

confidence: 99%

An Adaptive, Automatic Multiple-Case Deletion Technique for Detecting Influence in Regression

2014

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“…However, an excessively large value of ϵ can create swamping. Masking occurs when an outlying case is unidentified and misclassified as a good one, and swamping occurs when regular observations are incorrectly identified as outliers [15,43]. Experience of MLS data reveals that generally, the majority or more than 50% of points are inliers within a local neighbourhood.…”

Section: Proposed Methods For Outlier Detection and Robust Saliency Fmentioning

confidence: 96%

“…Hido et al [26] pointed that the solutions of the One-class Support Vector Machine (OSVM) and SVDD depend heavily on the choice of the tunning parameters and there seems to be no reasonable method to appropriately fix the values of the tuning parameters. Several survey papers [15,18,20,43] have been published in the last decade that explored a variety of algorithms covering the full range of statistics, machine learning and data mining techniques. Hodges and Austin [18] concluded: there is no single universally applicable or generic outlier detection approach.…”

Section: Outlier Detection and Robust Methodsmentioning

confidence: 99%

Outlier detection and robust normal-curvature estimation in mobile laser scanning 3D point cloud data

Nurunnabi

West

Belton

2015

Pattern Recognition

168

127

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a b s t r a c tThis paper proposes two robust statistical techniques for outlier detection and robust saliency features, such as surface normal and curvature, estimation in laser scanning 3D point cloud data. One is based on a robust z-score and the other uses a Mahalanobis type robust distance. The methods couple the ideas of point to plane orthogonal distance and local surface point consistency to get Maximum Consistency with Minimum Distance (MCMD). The methods estimate the best-fit-plane based on most probable outlier free, and most consistent, points set in a local neighbourhood. Then the normal and curvature from the best-fit-plane will be highly robust to noise and outliers. Experiments are performed to show the performance of the algorithms compared to several existing well-known methods (from computer vision, data mining, machine learning and statistics) using synthetic and real laser scanning datasets of complex (planar and non-planar) objects. Results for plane fitting, denoising, sharp feature preserving and segmentation are significantly improved. The algorithms are demonstrated to be significantly faster, more accurate and robust. Quantitatively, for a sample size of 50 with 20% outliers the proposed MCMD_Z is approximately 5, 15 and 98 times faster than the existing methods: uLSIF, RANSAC and RPCA, respectively. The proposed MCMD_MD method can tolerate 75% clustered outliers, whereas, RPCA and RANSAC can only tolerate 47% and 64% outliers, respectively. In terms of outlier detection, for the same dataset, MCMD_Z has an accuracy of 99.72%, 0.4% false positive rate and 0% false negative rate; for RPCA, RANSAC and uLSIF, the accuracies are 97.05%, 47.06% and 94.54%, respectively, and they have misclassification rates higher than the proposed methods. The new methods have potential for local surface reconstruction, fitting, and other point cloud processing tasks.

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“…The twice-the-mean rule and thrice-the-mean rule on the diagonal elements of the hat matrix have been reported in the literature to identify the leverage points. Reference [23] has mentioned the Cook's distance and Welsch and Kuh's distance to detect and identify the single leverage point. The Mahalanobis distance based on the projection pursuit algorithm for minimum volume ellipsoid cannot be applied to sparse systems.…”

Section: Detection Of Leverage and Bad Data Pointsmentioning

confidence: 99%

“…will not be able to identify the real high leverage points. Nurunnabi, Hadi and Imon in [23] have used a modified Cook's distance and Habshah, Norazan and Imon [24] have proposed a robust diagnostic potential to address this issue. Reference [24] have applied the technique on Hawkins, Bradu and Kass data and Brownlee's stack loss data to illustrate the simultaneous identification of outliers or erroneous data and high leverage points.…”

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confidence: 99%

Bad data detection in the context of leverage point attacks in modern power networks

Majumdar

2017

2017 IEEE Power &Amp; Energy Society General Meeting

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Abstract-This paper demonstrates a concept to detect bad data in state estimation when the leverage measurements are tampered with gross error. The concept is based on separating leverage measurements from non-leverage measurements by a technique called diagnostic robust generalized potential (DRGP), which also takes care of the masking or swamping effect, if any. The methodology then detects the erroneous measurements from the generalized studentized residuals (GSR). The effectiveness of the method is validated with a small illustrative example, standard IEEE 14-bus and 123-bus unbalanced network models and compared with the existing methods. The method is demonstrated to be potentially very useful to detect attacks in smart power grid targeting leverage points in the system. Index Terms-distribution management system (DMS), remote terminal unit (RTU), state estimation (SE), leverage measurements, bad data detection (BDD), generalized studentized residuals (GSR), diagnostic-robust generalized potentials (DRGP)

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Procedures for the identification of multiple influential observations in linear regression

Cited by 25 publications

References 24 publications

An Adaptive, Automatic Multiple-Case Deletion Technique for Detecting Influence in Regression

An Adaptive, Automatic Multiple-Case Deletion Technique for Detecting Influence in Regression

Outlier detection and robust normal-curvature estimation in mobile laser scanning 3D point cloud data

Bad data detection in the context of leverage point attacks in modern power networks

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