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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

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Maximal correlation and independence

Let $X$ and $Y$ be random variables. Then the maximal correlation $\rho_m(X;Y)$ is defined as $$ \rho_m (X;Y) := \max_{(f(X),g(Y))\in S} \mathbb{E} [f(X)g(Y)] $$ where $S$ is the collection of pairs …