Is there a version of Hoeffding's inequality for vector valued random variables?


This seems to be hard to find and I wonder why. I suppose it is difficult to show [Hoeffding's lemma](http://en.wikipedia.org/wiki/Hoeffding%27s_lemma), since the proof for the [inequality](http://en.wikipedia.org/wiki/Hoeffding%27s_inequality#Proof_of_Inequality) seems to translate relatively easy to a vector space.



Hoeffding's inequality for vector valued random variables
[Concentration Inequalities for Bounded Random Vectors](http://arxiv.org/abs/1309.0003), by Xinjia Chen (2013):



> 
> We derive simple concentration inequalities for bounded random
>  vectors, which generalize Hoeffding's inequalities for bounded scalar
>  random variables. As applications, we apply the general results to
>  multinomial and Dirichlet distributions to obtain multivariate
>  concentration inequalities.
> 
> 
> 


