A weighted Kendall's tau statistic

Shieh, Grace S.

doi:10.1016/s0167-7152(98)00006-6

Cited by 114 publications

(76 citation statements)

References 6 publications

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“…The ROCC were also weighted by production. In the case of Kendall's ROCC the product of weights for each data pair was used (Shieh 1998). The calculation of Kendall's ROCC is computationally demanding as it considers all data pairs individually, therefore the raster was randomly split into 100 equally sized data chunks and their ROCC were averaged.…”

Section: Contribution To Variancementioning

confidence: 99%

Modelling spatially explicit impacts from phosphorus emissions in agriculture

Scherer

Pfister

2015

Int J Life Cycle Assess

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Section: Contribution To Variancementioning

confidence: 99%

Modelling spatially explicit impacts from phosphorus emissions in agriculture

Scherer

Pfister

2015

Int J Life Cycle Assess

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“…Numerical Example: To illustrate our new weighted rank correlation, we use a data set, in Table 4, that was also used by [5] . The data set considers two techniques, A and B, used to select the most effective variables out of 20 variables for evaluation of some software packages.…”

Section: Resultsmentioning

confidence: 99%

“…For such cases, correlation measures that give more weighted for the top rankings were presented by [1,4,5] . To review these measures briefly, let {(X i , Y i ), 1 i n} be an independently and identically distributed (i.i.d.)…”

Section: Introductionmentioning

confidence: 99%

A New Weighted Rank Correlation

Coolen‐Maturi¹,

Abdelfattah²

2008

J. of Mathematics and Statistics

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Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract: Problem Statement: There have been many cases in real life where two independent sources have ranked n objects, with the interest focused on agreement in the top rankings. Spearman's rho and Kendall's tau coefficients assigned equal weights to all rankings. As a result, the literature proposed several weighted correlation coefficients with emphasis on the top rankings, including the top-down, weighted Kendall's Tau and Blest's correlation coefficient. Approach: This article introduced a new weighted rank correlation coefficient that was sensitive to agreement in the top rankings. It presented the limiting distribution under the null hypothesis of independence and provided a summary of quantiles of the exact null distribution for n = 3(1)9. Results: The article summarized the power comparison between the new weighted coefficient and other weighted coefficients, and showed that the new weighted rank correlation coefficient provided the locally most powerful rank test. Conclusions/Recommendations: The new weighted correlation should be used along with other weighted coefficients when the interest focused on agreement in the top rankings, in order to make an effective inference.

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“…This variant has been considered in the statistics literature as well. For example Shieh et al [18,19] give a version of Kendall's tau distance, where every inversion is weighted in proportion to the product of the two element weights. However, this work does not focus on its "metric"-like properties.…”

Section: Related Workmentioning

confidence: 99%

Generalized distances between rankings

Kumar

Vassilvitskii

2010

Proceedings of the 19th International Conference on World Wide Web

202

132

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Spearman's footrule and Kendall's tau are two well established distances between rankings. They, however, fail to take into account concepts crucial to evaluating a result set in information retrieval: element relevance and positional information. That is, changing the rank of a highly-relevant document should result in a higher penalty than changing the rank of an irrelevant document; a similar logic holds for the top versus the bottom of the result ordering. In this work, we extend both of these metrics to those with position and element weights, and show that a variant of the Diaconis-Graham inequality still holds -the generalized two measures remain within a constant factor of each other for all permutations.We continue by extending the element weights into a distance metric between elements. For example, in search evaluation, swapping the order of two nearly duplicate results should result in little penalty, even if these two are highly relevant and appear at the top of the list. We extend the distance measures to this more general case and show that they remain within a constant factor of each other.We conclude by conducting simple experiments on web search data with the proposed measures. Our experiments show that the weighted generalizations are more robust and consistent with each other than their unweighted counterparts.

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A weighted Kendall's tau statistic

Cited by 114 publications

References 6 publications

Modelling spatially explicit impacts from phosphorus emissions in agriculture

Modelling spatially explicit impacts from phosphorus emissions in agriculture

A New Weighted Rank Correlation

Generalized distances between rankings

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