Before revision:  We show that if the updates to the vector arrive in the random-order insertion-only model , then there exist space efficient algorithms with improved dependencies on the approximation parameter \varepsilon . In particular, for any real p > 2, we first obtain an algorithm for F_p moment estimation using \frac{1{\varepsilon^{4/p}}\cdot n^{1-2/p}} bits of memory.
After revision:  We show that if the updates to the vector arrive in the random-order insertion-only model  \frac{1{\varepsilon^{4/p}}\cdot n^{1-2/p}} bits of memory.