Kendall, M. & Gibbons, J.D. (1990) Rank Correlation Methods, 5th edn. Edward Arnold, London, UK.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are distinct, the authority weights induce a total ranking of the elements in P . If the weights are not all distinct, then we have a partial ranking of the elements in P . We will also refer to total rankings as permutations. The problem of comparing permutations has been studied extensively [30, 16, 18]. One popular distance measure is the Kendall s tau distance which captures the number of disagreements between the rankings. Let denote the set of all pairs of nodes. Let a 1 , a 2 be two LAR vectors. We define the violating set, as follows j) a 1 (i) a 1 (j) a 2 (i) a ....

M. G. Kendall. Rank Correlation Methods. Griffin, London, 1970.

....the one considered by Tchen. One of our objectives in this paper is to provide a uni ed characterization by functional inequalities for three di erent notions of positive dependence: i) total positivity of order 2, ii) stochastic increasingness and (iii) positive quadrant dependence. Kendall [15] introduced a measure of correlation for a bivariate random vector X = X 1 ; X 2 ) by comparing two pairs of independent random vectors X with the same joint distribution as X. The measure, known as Kendall s , is de ned as follows: P ( X 2 ) 0) P ( X 2 ) 0) ....

KENDALL, M.G. (1962). Rank correlation methods. Charles Grin and Co., London.

....are not completely in agreement with each other regarding the definition of the scaling parameters. To test how much the stakeholders agree with each other regarding the scaling parameters, we use the Kendall s concordance coefficient as a measure of agreement for the group as a whole [Kendall 55] The more the group agrees over the rank of each attribute, the higher the concordance coefficient. In the example shown in Table 2, we have 3 stakeholders and 4 attributes. The values in the columns show the elicited scaling parameters and the numbers in the bracket show the rank It is similar ....

Kendall, M.G. Rank Correlation Methods. London: C. Griffin, 1955.

.... of measures of association for data is an important issue in many quantitative problems arising in diverse disciplines such as political science, psychology and sociology; and in rank statistics, Kendall s and Spearman s ae are commonly used measures of association (or disarray) of data; cf. [11, 22, 29]. In probability theory, the Kolmogorov distance and the total variation distance between two distributions are frequently used measures of closeness. This paper is concerned with problems of the following type: Accepted for publication in Advances in Applied Mathematics. Given a random (under ....

M. Kendall and J. D. Gibbons. Rank correlation methods . Edward Arnold, London, fifth edition, (1990).

.... of measures of association for data is an important issue in many quantitative problems arising in diverse disciplines such as political science, psychology and sociology; and in rank statistics, Kendall s # and Spearman s # are commonly used measures of association (or disarray) of data; cf. [11, 22, 29]. In probability theory, the Kolmogorov distance and the total variation distance between two distributions are frequently used measures of closeness. This paper is concerned with problems of the following type: # Accepted for publication in Advances in Applied Mathematics. Given a random (under ....

M. Kendall and J. D. Gibbons. Rank correlation methods. Edward Arnold, London, fifth edition, (1990).

....order of an unordered item set. We denote an unordered item set by , and its estimated order by OU . Note that attribute value vectors of items in the unordered set are known. In order to directly evaluate the errors in orders, we adopt the Spearman s Rank Correlation Coefficient or the # [3]. The # is the correlation between ranks of items. The rank, r(O, x) is the cardinal number that indicates the position of I in the order O. For example, for the order O=I , the r(O, 3) 1 and the r(O, 2) 3. If no tie in rank is allowed, the # between two orders, O i and O i , can ....

M. Kendall and J. D. Gibbons. Rank Correlation Methods. Oxford University Press, fifth edition, 1990.

....methods in comparing top k lists. Methodology. A special case of a top k list is a full list, that is, a permutation of all of the objects in a fixed universe. There are several standard methods for comparing two permutations, such as Kendall s tau and Spearman s footrule (see the textbooks [KG90, Dia88] We cannot simply apply these known methods, since they deal only with comparing one permutation against another over the same elements. Our first (and most important) class of distance measures between top k lists is obtained by various natural modifications of these standard notions of ....

....top k lists introduced in Section 3 is a metric or a near metric. In Section 6, we give an algorithmic application that exploits distance measures being in the same equivalence class. 2 Metrics on permutations The study of metrics on permutations is classical. The book by Kendall and Gibbons [KG90] provides a detailed account of various methods. Diaconis [Dia88] gives a formal treatment of metrics on permutations. We now review two well known notions of metrics on permutations. A permutation oe is a bijection from a set D = D oe (which we call the domain, or universe) onto the set [n] ....

M. Kendall and J. D. Gibbons. Rank Correlation Methods. Edward Arnold, London, 1990.

.... 2 (f 4) z Gamma P oi where the different factors are: f = 1 2 (n g Gamma 1) n h (n h Gamma 1) B.4) 2 = 1 48ae n h (n h Gamma 1) n h Gamma 1) n h 2) Gamma 6 (n g Gamma 1) 1 Gamma ae) B. 2 Rank Correlations Rank correlations [32] are correlations in connection with ordinal data. Here I will describe 2 rank correlations which both are particular cases of the general correlation coefficient. The data ranks should here be described by integers from one to the number of elements. The following example is from [32] Boys A B ....

....correlations [32] are correlations in connection with ordinal data. Here I will describe 2 rank correlations which both are particular cases of the general correlation coefficient. The data ranks should here be described by integers from one to the number of elements. The following example is from [32]: Boys A B C D E F G H I J Math 7 4 3 10 6 2 9 8 1 5 Music 5 7 3 10 1 9 6 2 8 4 (B.5) Here are 10 boys abilities in mathematics and music put in 2 ordinal rankings. A rank correlation should tell if a boy being bright in mathematics is likely to be musical compared to the other 9. B.2.1 ....

Maurice G. Kendall. Rank Correlation Methods. Griffin, London, 4. edition, 1970.

....most information retrieval researchers agree that binary relevance is very coarse and that it is merely used as as simplifying assumption. Since the method presented in the following does not require such a simplification, we will depart from a binary relevance scheme and adapt Kendall s [19][21] as a per formance measure. For comparing the ordinal correlation of two random variables, Kendall s is the most frequently used measure in statistics. For two finite strict orderings ra C D x D and rb C D x D, Kendall s can be defined based on the number P of concordant pairs and the ....

M. Kendall. Rank Correlation Methods. Hafner, 1955.

.... that 5 5 , and therefore, the measure , which is analogous to (56) is constant, irrespective of the possible connections between the orders on ( and ( The statistics are related to the well known Kendall s statistic [16] via # (63) The value of is bounded by . A value of near can only appear if most of the pairs of elements are collected in the statistic, which is interpreted as a high positive monotone correlation of ( with ( A ....

Kendall, M. G. (1970). Rank correlation methods. London: Charles Griffin.

....q=0 2 q 3 8 (1 2 q ) 4 O(1 n) 3 7 O(1 n) # However, this lower bound is very likely not the best possible. The rank correlation # between two independently chosen linear orders on m elements is nearly normally distributed with expected value 0 and standard deviation O(1 # m) cf. [KG90]) Hence (# 1) 2 has expected value 1 2, which motivates the following conjecture. Conjecture 12 Every finite metric space can be mapped into E 1 with accuracy # 1 2. 13 ....

Maurice Kendall and Jean Dickinson Gibbons, Rank correlation methods, 5th ed., Edward Arnold, London, 1990.

....between the degree of technical integration, the degree of organizational integration, and the level of benefit achieved. To analyze this rank correlation the Kendall coefficient of concordance W is utilized as a statistical measure because it can be used for several rankings and for tied ranks [7]. If all ranks are in complete agreement the coefficient W = 1. If they differ completely then W = 0. Because there are three rankings, a positive or negative correlation cannot be established. The calculation of W was found to be: W = 0.60 14 The statistical significance of the correlation ....

Kendall, M., and Dickinson Gibbons, J. Rank Correlation Methods. 5 th Edition, London: Edward Arnold, 1990. 19

....order into consideration there is a need for a new similarity measure. Recently, Fagin et al. 4] inspired by the question of measuring the goodness of our pruning approach, developed various correlation methods for comparing the top k in two lists, based on methods for comparing two permutations [7]. For our experiments, we used one of their variations of Kendall s tau method. The original Kendall s tau method for comparing two permutations assigns a penalty S(i, j) 1 for each pair i, j of distinct items for which i appears before j in one permutation and j appears before i in the other ....

M. Kendall and J. D. Gibbons. Rank correlation methods. Edward Arnold, London, 5th edition, 1990.

....such a case of ranking output of documents gathered by web search engines. For a set of documents, accordance between relevance ranking computed by a pro le and relevance ranking judged by a user can be measured by rank correlation between two rankings. The coe cient of Kendall s rank correlation [7] is a statistic that gives the strength of rank correlation, and it takes a value between 1 and 1. By using the coe cient of Kendall s rank correlation, we can test statistical hypotheses whether these two rankings are independent or not, and whether these two rankings have positive correlation or ....

Kendall, M.G.: Rank Correlation Methods. Charles Grin (1970)

....the verification decision. Such a distribution would be difficult to obtain under hypotheses other than independence, which would clearly not be useful here when testing statistical dependence. The image congruence is measured by Spearman coefficient of concordance K among m vectors of length n [11] K = 12 m(m Gamma 1)n(n 2 Gamma 1) n X i=1 0 m X j=1 r ij 1 A 2 Gamma 3m(n 1) Gamma n 1 (m Gamma 1) n Gamma 1) 1.7) Accurate Natural Surface Reconstruction from Polynocular Stereo 11 where r ij 2 f1; 2; ng is the rank of the i th point projected to j th ....

....up to an unknown monotonic transformation. 2. To relieve the influence of image texture statistical distribution on the congruence measure distribution. Note that, under the hypothesis of independence, the statistical distribution of K is invariant to the statistical distribution of image values [11]. Under hypotheses other than independence, this is no longer true, but the sensitivity of K to the distribution is small. This is important given the enormous variability of real world texture distributions. The original (unrectified) images are used in the verification test in order to ....

M. Kendall and J. D. Gibbons. Rank Correlation Methods. Edward Arnold, 1990.

....an expanding ball. As we should expect, this Euclidean version of Kemeny s method favors BC over KR outcomes. But stopping at the first transitive ranking region rather than the transitivity plane generates n # 4 situations where its outcomes di#er from the BC. As another consequence, Kendall [8] characterizes the BC (in statisics called the Kendall method ) with the Euclidean distance; about fifteen years later Farkas and Nitzan [5] rediscovered the same condition. 7 The reader can use Fig. 1 to show that the l 1 distance would define a square in the transitivity plane with qBC at its ....

M. G. Kendall, Rank Correlation Methods, (Chaps. 6, 7) Hafner, New York, 1962.

....Standard Correlation Coe#cient [3] is invariant to a linear transformation acting on image values. It is computed as a mean of all pairwise correlation coe#cients and has a range of [ 1, 1] It allows to suppress the influence of small deviations from surface non Lambertianity. A Rank Correlation [2] is more general since it enables any monotonic transformation among the images. We use Spearman s Rank Concordance [2] Let R ij be the rank of point i among the values collected in image j, the R ij ranges from 1 to the total number of measurements n. Let R i = # m j=1 R ij be the sum of ....

....mean of all pairwise correlation coe#cients and has a range of [ 1, 1] It allows to suppress the influence of small deviations from surface non Lambertianity. A Rank Correlation [2] is more general since it enables any monotonic transformation among the images. We use Spearman s Rank Concordance [2]. Let R ij be the rank of point i among the values collected in image j, the R ij ranges from 1 to the total number of measurements n. Let R i = # m j=1 R ij be the sum of ranks of the same point over all images. It is easy to prove that the mean value of R i is R = 1 2 m(n 1) Kendall s ....

M. Kendall and J. D. Gibbons. Rank Correlation Methods. Edward Arnold, 1990.

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Kendall, M.; Gibbons, J.D. Rank correlation methods. Oxford: Oxford University Press, 1990.

....= GammaK n (t) From Robillard (1972, eqn. 1.4) it follows that K u (t) 0 and K v (t) 0. Hence log(x) GammaK n (t) Silverstone (1950) established that GammaK n (t) 1 2 oe 2 n t 2 1 n Gamma 1 oe 4 n t 4 ; 12) where oe 2 n = Var (S n ) has been previously derived by Kendall (1975) and is given below by eqn. 23) Let Delta 1 0 be the real positive solution to 1 2 oe 2 n Delta 2 1 1 n Gamma 1 oe 4 n Delta 4 1 = log(2) 13) Then for 0 t Delta 1 , we have 0 x 2 and hence, log(x) 1 X =1 ( Gamma1) 1 (x Gamma 1) 14) Now we can ....

....(it) j =j in the expansion of e itS u ; v ;A 0 B P 1 h=1 i Gamma P i P j Ka ij (t) j h h 1 C A : Since y is the cf of S u ;v for which all moments exist and since S u ;v has mean zero and variance oe 2 u ;v given below in eqn. 29) as well as in Kendall (1975), we obtain using a well known expansion for cf s (Lo eve, 1963, p.200) y = 1 Gamma 1 2 oe 2 u ;v t 2 o(t 2 ) as t 0: 16) Hence there is a Delta 2 0 such that jy Gamma 1j 1 when 0 t Delta 2 . Taking 0 t min( Delta 1 ; Delta 2 ) we have jx Gamma 1j 1 and jy ....

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Kendall, M.G. (1975). Rank Correlation Methods (4th ed). London: Griffin.

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Kendall, M. & Gibbons, J.D. (1990) Rank Correlation Methods, 5th edn. Edward Arnold, London, UK.

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M. Kendall, Rank Correlation Methods, Charles Gri#n and Co., London, 1970.

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Kendall, M. and J. Gibbons (1990). Rank correlation methods (Fifth ed.). London: Edward Arnold.

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M.G. Kendall. Rank Correlation Methods. Charles Griffin, London, 1948.

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Kendall, M. & Gibbons, J.D. (1990) Rank Correlation Methods, 5th edn. Edward Arnold, London, UK.

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KENDALL, M. G. Rank Correlation Methods. Charles Griffin & Company, 1962.

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M. Kendall and J. Gibbons. Rank Correlation Methods. Edward Arnold, London, 5 edition, 1990.

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Kendall, M. & Gibbons, K. D. (1990). Rank Correlation Methods. Oxford University Press, fifth edition.

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KENDALL, M. 1975. Rank Correlation Methods, 4th ed. Griffin Ltd.

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Kendall, M. and J. D. Gibbons, 1990. Rank Correlation Methods. Edward Arnold, London.

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Maurice G. Kendall. Rank Correlation Methods. Griffin, London, 4th edition, 2nd impression, 1975.

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Maurice G. Kendall. Rank Correlation Methods. Hafner Publishing Co., New York, 1955.

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M. Kendall and J. D. Gibbons. Rank Correlation Methods. Oxford University Press (fifth edition)., 1990.

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M. G. Kendall, Rank Correlation Methods, 4th ed, London, U.K.: Griffin, 1970.

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M. G. Kendall, J. D. Gibbons. "Rank Correlation Methods ", Edward Arnold, London, 1990.

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Maurice G. Kendall. Rank Correlation Methods. Hafner Publishing Co., New York, 1955.

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Maurice Kendall and Jean Dickinson Gibbons. Rank Correlation Methods. Edward Arnold, 1990.

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Kendall, M., Gibbons, J.D.: Rank Correlation Methods. fifth edn. Oxford University Press (1990)

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M. Kendall and J. D. Gibbons. Rank Correlation Methods. Oxford University Press, fifth edition, 1990.

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M.G. Kendall and J.D. Gibbons, Rank correlation methods, London: Edward Arnold, 1990.

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M. G. Kendall, Rank Correlation Methods. Griffin, 1970. 51

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M. Kendall and J. D. Gibbons. Rank Correlation Methods. Edward Arnold, 1990.

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M. G. Kendall, Rank Correlation Methods, 4th ed, London, U.K.: Griffin, 1970.

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M. Kendall and J. D. Gibbons. Rank Correlation Methods. Edward Arnold, fifth edition, 1990.

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M. Kendall and J. D. Gibbons. Rank correlation methods. Edward Arnold, 1990.

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Kendall, M. G. (1970) Rank Correlation Methods. London: Griffin.

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Kendall M, Gibbons JD. Rank correlation methods. 5th ed. New York, NY: Oxford University Press, 1990; 8 --10.

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Kendall, M. and Gibbons, J. D. (1990). Rank Correlation Methods, fifth ed. New York: Edward Arnold.

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Kendall, M. and Gibbons, J.D. Rank Correlation Methods. 1990. 5th edition. Edward Arnold, London. 33

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Kendall, M. & Gibbons, J. Rank Correlation Methods, Oxford Univ. Press, 1990.

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Maurice G. Kendall. Rank Correlation Methods. Charles Grin and Company, 1962. 452

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