The Wikipedia entry on this topic is, to me, very confusing. It states that:
If X1, ...., Xn are independent and have a Poisson distribution with parameter λ, then the sum T(X) = X1 + ... + Xn is a sufficient statistic for λ.
I know that $T(X)$ is the "sufficient statistic" function, but I am lost as to what "sum T(X)" means in this context. The sum of my iid observations? What does that even mean if they are N-dimensional?
The demonstration below this line is also confusing (to me) and even mentions a function "h(x)" which is never explained as far as I can see.
Could you explain the concept of "sufficient statistic" for a Poisson distributed sample better?