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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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bracketing number vs covering number

Your elaboration is essentially right, except the brackets themselves are not $\|\cdot\|$-balls. If $[l,u]$ is a $2\epsilon$-bracket, then it is contained in the $\|\cdot\|$-ball of radius $\epsilon$ …
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