A Rademacher comparison theorem?

June 30th, 2008 ~ Posted in: Mathematics

Given Rademacher variables \epsilon_j , what can we say about
 \mathbb{E} \sup_{c > a_j \geq 0} \left|\sum_{i=1}^n \epsilon_j a_j \right| versus \mathbb{E} \sup_{c >a_j \geq 0} \sum_{i=1}^n \epsilon_j a_j ?

Anything?

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