Remarks on the Maximum Correlation Coefficient

Department of Mathematics, Stanford University, Palo Alto, California, United States
Bernoulli (Impact Factor: 1.16). 06/2000; 7(2). DOI: 10.2307/3318742
Source: OAI


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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    • "If, we restrict ϕ 1 , ϕ 2 to linear function, then MCC is the classical Pearson correlation coefficient, For further discussion on maximum correlation coefficient we refer to [2], [11]. "
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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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    • "Another exception is provided by the surprising result of Dembo et al. (2001), and its subsequent extensions given by Bryc et al. (2005) and Yu (2008). In its general form the result states that for any independent identically distributed (i.i.d.) nondegenerate r.v.'s X 1 , "
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    ABSTRACT: We provide a method that enables the simple calculation of the maximal correlation coefficient of a bivariate distribution, under suitable conditions. In particular, the method readily applies to known results on order statistics and records. As an application we provide a new characterization of the exponential distribution: Under a splitting model on independent identically distributed observations, it is the (unique, up to a location-scale transformation) parent distribution that maximizes the correlation coefficient between the records among two different branches of the splitting sequence.
    Journal of Multivariate Analysis 04/2012; DOI:10.1016/j.jmva.2013.03.017 · 0.93 Impact Factor
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    • "The proof given by Lancaster (1957) utilizes series expansion involving Hermite polynomials. More recently, Dembo et al. (2001) have shown that the maximal correlation between two partial sums of independent and identically distributed random variables is also their usual correlation. Specifically, if non-degenerate random variables X 1 , . . . "
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    ABSTRACT: A well-known theorem states that the maximal correlation between a pair of bivariate normal random variables equals the absolute value of their ordinary (Pearson) correlation. This work provides a short new proof, besides establishing some results regarding the maximal correlation coefficient in general.
    Statistics [?] Probability Letters 07/2008; 78(9):1072-1075. DOI:10.1016/j.spl.2007.10.006 · 0.60 Impact Factor
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