a) , so that one can write
Then, for any ,
Remark: Observing that , and plugging these expressions into the bound, one obtains immediately the Bernstein inequality under the hypotheses of boundness of random variables, as one might expect. However, Bernstein inequalities, although weaker, hold under far more general hypotheses than Bennett one.
|Date of creation||2013-03-22 16:12:25|
|Last modified on||2013-03-22 16:12:25|
|Owner||Andrea Ambrosio (7332)|
|Last modified by||Andrea Ambrosio (7332)|
|Author||Andrea Ambrosio (7332)|