On the asymptotic distribution of a general measure of monotone dependence

Cifarelli, Donato Michele; Conti, Pier Luigi; Regazzini, Eugenio

doi:10.1214/aos/1032526975

Cited by 26 publications

(21 citation statements)

References 9 publications

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“…As shown in Cifarelli et al (1996), both Spearman's and Gini's measures can be considered as special cases of the following general cograduation measure…”

Section: Testing For No Relationships Between Two Variablesmentioning

confidence: 99%

On the Estimation of the Distribution Function of a Finite Population Under High Entropy Sampling Designs, with Applications

Conti

2014

Sankhya B

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The estimation of the distribution function of a population is an important problem in sampling finite populations. The existing literature focuses on the problem of estimating the population distribution function (p.f.d.) at a single point, or at a finite number of points. In this paper the main interest consists in estimating the whole p.d.f.. In many respects, the starting point is close to classical nonparametric statistics, although the approach to inference is based on sampling design. It is shown here that the Hajek estimator of the p.d.f., if properly centered and scaled, converges weakly to a Gaussian process with covariance kernel proportional to that of a Brownian bridge. The proportionality factor essentially depends on the sample design. Applications to (i) construction of a confidence band for the p.d.f., (ii) comparison of the p.d.f.s of two populations, and (iii) testing for independence of two characters are provided

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“…As shown in Cifarelli et al (1996), both Spearman's and Gini's measures can be considered as special cases of the following general cograduation measure…”

Section: Testing For No Relationships Between Two Variablesmentioning

confidence: 99%

On the Estimation of the Distribution Function of a Finite Population Under High Entropy Sampling Designs, with Applications

Conti

2014

Sankhya B

Self Cite

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“…when the marginal components are independent; 2 moreover, differently from other common measures of monotone dependence, D(H 0 ) = D((H − + H + )/2), that is the functional does not consider symmetrically positive and negative dependence. Following Cifarelli and Regazzini (1990), a measure of monotone dependence should be defined so that it vanishes in case of indifference, that is, roughly speaking, for such situations characterized by a compensation of the departure from H + and the departure from H − ; special cases of indifference are then independence and Cifarelli and Regazzini (1990) and Cifarelli et al (1996) for further details]. The measure D(H) may of course be modified to vanish in case of independence but it cannot take the same value for each situation termed as indifference.…”

Section: Distribution Of D Under Independencementioning

confidence: 99%

“…, n). Another measure of rank correlation is Gini's cograduation index: (Gini 1954; see also Cifarelli et al 1996), where the normalization constant g equals n 2 when n is even and n 2 − 1 when n is odd. When m > 2, the judges may all agree about the n objects but they cannot completely disagree.…”

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confidence: 99%

A test of concordance based on Gini’s mean difference

Borroni

Zenga

2006

Stat. Meth. & Appl.

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“…Actually G(H ) belongs to a wide class of association measures studied by Cifarelli et al (1996), which in fact includes the population version of ρ n as well. These measures share the property of vanishing for the elements of the Fréchet class named (again after Corrado Gini) as indifferent, that is when…”

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confidence: 99%

“…This lack of "symmetry" can then be regarded as a drawback to be corrected. Cifarelli et al (1996) show that a functional vanishing at indifference can be defined by subtracting a corresponding discordance measure from a given concordance measure (see Cifarelli and Regazzini 1990 for further details). Roughly speaking, a concordance measure is a distance of a given cdf from the minimum element of the Fréchet class.…”

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confidence: 99%

A new rank correlation measure

Borroni

2011

Stat Papers

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A new rank correlation measure β n is proposed, so as to develop a nonparametric test of independence for two variables. β n is shown to be the symmetrized version of a measure earlier proposed by Borroni and Zenga (Stat Methods Appl 16:289-308, 2007). More specifically, β n is built so that it can take the opposite sign, without changing its absolute value, when the ranking of one variable is reversed. Further, the meaning of the population equivalent of β n is discussed. It is pointed out that this latter association measure vanishes not only at independence but, more generally, at indifference, that is when the two variables do not show any "tendency" to positive or negative dependence. The null distribution of β n needs an independent study: hence, the finite null variance and a table of critical values are determined. Moreover, the asymptotic null distribution of β n is derived. Finally, the performance of the test based on β n is evaluated by simulation. β n is shown to be a good competitor of some classical tests for the same problem.

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On the asymptotic distribution of a general measure of monotone dependence

Cited by 26 publications

References 9 publications

On the Estimation of the Distribution Function of a Finite Population Under High Entropy Sampling Designs, with Applications

On the Estimation of the Distribution Function of a Finite Population Under High Entropy Sampling Designs, with Applications

A test of concordance based on Gini’s mean difference

A new rank correlation measure

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