A Simple Method for Obtaining the Maximal Correlation Coefficient and Related Characterizations

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 (to appear, 19 pages)

References in corpus (1)

• An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds

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