Abstract
A new upper bound on P(a1η1 +a2η2 + ... x) is obtained, where η1,η2,...are independent zero-mean random variables such that |ηi| 1f or alli. A multidimensional ana- logue of this result and extensions to (super)martingales are presented, as well as an application to self-normalized sums (or, equivalently, to t -statistics).
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