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A simple method for obtaining the maximal correlation coefficient and related characterizations

Research output: Contribution to journalJournal article

Published

Journal publication date07/2013
JournalJournal of Multivariate Analysis
Volume118
Number of pages13
Pages102-114
Early online date6/04/13
Original languageEnglish

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.