Sharp Lower Bound on the Minimax Risk for Multinomial Uniformity Testing via a Conditional Central Limit Theorem

Alon Kipnis

We study minimax goodness-of-fit testing for uniformity from $n$ multinomial observations over $N$ categories against ${\ell }_p$ departures of size ${\epsilon }_n$. Writing $u_n:=ε_n^2 n\,N^{3…