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Maximum correlations and tests of goodness-of-fit. (English) Zbl 1135.62343
Cuadras, Carles M. (ed.) et al., Distributions with given marginals and statistical modelling. Papers presented at the meeting, Barcelona, Spain, July 17–20, 2000. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0914-3/hbk). 113-124 (2002).
Summary: Hoeffding’s maximum correlation coefficient equals unity when both distributions coincide. This fact suggests a method to test whether the cdf of an iid sequence of random variables is a given $$F$$, by computing this coefficient between $$F$$ and the empirical cdf of the sequence. In this paper we present three instances of actual goodness-of-fit tests derived from this basic principle and we discuss their small- and large-sample properties.
For the entire collection see [Zbl 1054.62002].
##### MSC:
 62H20 Measures of association (correlation, canonical correlation, etc.) 62G10 Nonparametric hypothesis testing 62G30 Order statistics; empirical distribution functions