 Bennett inequality

ID: bennett-inequality

If independent centered random variables satisfy

X_{i} \leq b

and

\sum_{i} E X_{i}^{2} \leq v

, then

P (\sum_{i} X_{i} \geq t) \leq exp [- \frac{v}{b ^{2}} h (\frac{b t}{v})], h (u) = (1 + u) lo g (1 + u) - u .

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