Remarks on the maximum correlation coefficient

Bernoulli (Impact Factor: 0.94). 06/2000; DOI: 10.2307/3318742
Source: OAI

ABSTRACT The maximum correlation coefficient between partial sums of independent and identically distributed random variables with finite second moment equals the classical (Pearson) correlation coefficient between the sums, and thus does not depend on the distribution of the random variables. This result is proved, and relations between the linearity of regression of each of two random variables on the other and the maximum correlation coefficient are discussed.

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    ABSTRACT: We proposed a new statistical dependency measure called Copula Dependency Coefficient(CDC) for two sets of variables based on copula. It is robust to outliers, easy to implement, powerful and appropriate to high-dimensional variables. These properties are important in many applications. Experimental results show that CDC can detect the dependence between variables in both additive and non-additive models.
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    ABSTRACT: In the first part of this review article some recent developments of maximal correlation coefficient, introduced by Gebelein (1941) [7], and its applications in various areas of statistics are discussed. The second part is devoted to find the distributions providing the maximal correlation coefficient between generalized order statistics (gos) and dual generalized order statistics (dgos), which are introduced by Kamps (1995) [8] and Burkschat et al. (2003) [4], respectively. Finally, in the third part, general theorems are presented, which give simple non-parametric criterion for the asymptotic independence between the different elements of gos, as well as dgos.
    Journal of the Egyptian Mathematical Society. 01/2011; 19(s 1–2):28–32.
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    ABSTRACT: In each of three exhaustive and distinct cases, it is found a distribution for which the correlation coefficient between the elements of the generalized order statistics (gos) is maximal. The corresponding result for the dual generalized order statistics (dgos) is derived for other three different distributions. Moreover, some interesting relations for the regression curves between the elements of gos and dgos based on these distributions are obtained. As a consequence of this result, a non-parametric criterion of independence between gos and between dgos in a general setting is derived.
    Arabian Journal of Mathematics. 01/2012; 1(2).


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