Let $X$ be $n$-dimensional s.t. $X_j\sim Poiss(\lambda_j)$. The components are independent, but the rates are different.

I am interested in bounds for $\Pr(||X-\lambda||\geq y)$, where $\lambda$ is the vector of rates and $||\cdot||$ is some norm. I can use the $1$-norm, but other norms are welcome too.

I bet there are many results out there, but I couldn't find the right term. Can somebody provide pointers?

In particular, I don't want to derive the Chernoff bounds myself, since I'm sure people spent a lot of time trying to come up with good bounds.

Thanks!

Your Answer

 

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.